Господин Экзамен
Общий знаменатель (5*(cos(pi/2-2*pi/14)-sin(pi/14)))/(cos(pi/7)*sin(pi/14))
Решение
Вы ввели
[src]
/ /pi 2*pi\ /pi\\
5*|cos|-- - ----| - sin|--||
\ \2 14 / \14//
----------------------------
/pi\ /pi\
cos|--|*sin|--|
\7 / \14/
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \cos{\left(- \frac{2 \pi}{14} + \frac{\pi}{2} \right)}\right)}{\sin{\left(\frac{\pi}{14} \right)} \cos{\left(\frac{\pi}{7} \right)}}$$
5*(cos(pi/2 - 2*pi/14) - sin(pi/14))/((cos(pi/7)*sin(pi/14)))
Общее упрощение
[src]
/pi\
5*tan|--|
5 \7 /
- ------- + ---------
/pi\ /pi\
cos|--| sin|--|
\7 / \14/
$$- \frac{5}{\cos{\left(\frac{\pi}{7} \right)}} + \frac{5 \tan{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{14} \right)}}$$
-5/cos(pi/7) + 5*tan(pi/7)/sin(pi/14)
Рациональный знаменатель
[src]
/pi\ /pi\
- 5*sin|--| + 5*sin|--|
\14/ \7 /
-----------------------
/pi\ /pi\
cos|--|*sin|--|
\7 / \14/
$$\frac{- 5 \sin{\left(\frac{\pi}{14} \right)} + 5 \sin{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{14} \right)} \cos{\left(\frac{\pi}{7} \right)}}$$
/5*pi\
5*cos|----|
5 \ 14 /
- ------- + ---------------
/pi\ /pi\ /pi\
cos|--| cos|--|*sin|--|
\7 / \7 / \14/
$$- \frac{5}{\cos{\left(\frac{\pi}{7} \right)}} + \frac{5 \cos{\left(\frac{5 \pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)} \cos{\left(\frac{\pi}{7} \right)}}$$
-5/cos(pi/7) + 5*cos(5*pi/14)/(cos(pi/7)*sin(pi/14))
Общий знаменатель
[src]
/pi\ /pi\
- 5*sin|--| + 5*sin|--|
\14/ \7 /
-----------------------
/pi\ /pi\
cos|--|*sin|--|
\7 / \14/
$$\frac{- 5 \sin{\left(\frac{\pi}{14} \right)} + 5 \sin{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{14} \right)} \cos{\left(\frac{\pi}{7} \right)}}$$
(-5*sin(pi/14) + 5*sin(pi/7))/(cos(pi/7)*sin(pi/14))
Собрать выражение
[src]
/ /pi\ /5*pi\\ /pi\ /pi\ 5*|- sin|--| + cos|----||*csc|--|*sec|--| \ \14/ \ 14 // \14/ \7 /
$$5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \cos{\left(\frac{5 \pi}{14} \right)}\right) \csc{\left(\frac{\pi}{14} \right)} \sec{\left(\frac{\pi}{7} \right)}$$
5*(-sin(pi/14) + cos(5*pi/14))*csc(pi/14)*sec(pi/7)
Степени
[src]
/pi\ /pi\
- 5*sin|--| + 5*sin|--|
\14/ \7 /
-----------------------
/pi\ /pi\
cos|--|*sin|--|
\7 / \14/
$$\frac{- 5 \sin{\left(\frac{\pi}{14} \right)} + 5 \sin{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{14} \right)} \cos{\left(\frac{\pi}{7} \right)}}$$
/pi\ /5*pi\
- 5*sin|--| + 5*cos|----|
\14/ \ 14 /
-------------------------
/pi\ /pi\
cos|--|*sin|--|
\7 / \14/
$$\frac{- 5 \sin{\left(\frac{\pi}{14} \right)} + 5 \cos{\left(\frac{5 \pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)} \cos{\left(\frac{\pi}{7} \right)}}$$
/ /pi\ /5*pi\\
5*|- sin|--| + cos|----||
\ \14/ \ 14 //
-------------------------
/pi\ /pi\
cos|--|*sin|--|
\7 / \14/
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \cos{\left(\frac{5 \pi}{14} \right)}\right)}{\sin{\left(\frac{\pi}{14} \right)} \cos{\left(\frac{\pi}{7} \right)}}$$
/ -5*pi*I 5*pi*I / -pi*I pi*I\\
| ------- ------ | ------ ----||
| 14 14 | 14 14 ||
|e e I*\- e + e /|
10*I*|-------- + ------- + ---------------------|
\ 2 2 2 /
-------------------------------------------------
/ -pi*I pi*I\
| ------ ----| / -pi*I pi*I\
| 7 7 | | ------ ----|
|e e | | 14 14 |
|------- + -----|*\- e + e /
\ 2 2 /
$$\frac{10 i \left(\frac{e^{- \frac{5 i \pi}{14}}}{2} + \frac{i \left(- e^{- \frac{i \pi}{14}} + e^{\frac{i \pi}{14}}\right)}{2} + \frac{e^{\frac{5 i \pi}{14}}}{2}\right)}{\left(\frac{e^{- \frac{i \pi}{7}}}{2} + \frac{e^{\frac{i \pi}{7}}}{2}\right) \left(- e^{- \frac{i \pi}{14}} + e^{\frac{i \pi}{14}}\right)}$$
10*i*(exp(-5*pi*i/14)/2 + exp(5*pi*i/14)/2 + i*(-exp(-pi*i/14) + exp(pi*i/14))/2)/((exp(-pi*i/7)/2 + exp(pi*i/7)/2)*(-exp(-pi*i/14) + exp(pi*i/14)))
Комбинаторика
[src]
/ /pi\ /5*pi\\
5*|- sin|--| + cos|----||
\ \14/ \ 14 //
-------------------------
/pi\ /pi\
cos|--|*sin|--|
\7 / \14/
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \cos{\left(\frac{5 \pi}{14} \right)}\right)}{\sin{\left(\frac{\pi}{14} \right)} \cos{\left(\frac{\pi}{7} \right)}}$$
5*(-sin(pi/14) + cos(5*pi/14))/(cos(pi/7)*sin(pi/14))
Объединение рациональных выражений
[src]
/ /pi\ /5*pi\\
5*|- sin|--| + cos|----||
\ \14/ \ 14 //
-------------------------
/pi\ /pi\
cos|--|*sin|--|
\7 / \14/
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \cos{\left(\frac{5 \pi}{14} \right)}\right)}{\sin{\left(\frac{\pi}{14} \right)} \cos{\left(\frac{\pi}{7} \right)}}$$
5*(-sin(pi/14) + cos(5*pi/14))/(cos(pi/7)*sin(pi/14))
Тригонометрическая часть
[src]
/pi\
5*tan|--|
/pi\ \7 /
- 5*sec|--| + ---------
\7 / /pi\
sin|--|
\14/
$$- 5 \sec{\left(\frac{\pi}{7} \right)} + \frac{5 \tan{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{14} \right)}}$$
/pi\
5*tan|--|
5 \7 /
- ------- + ---------
/pi\ /pi\
cos|--| sin|--|
\7 / \14/
$$- \frac{5}{\cos{\left(\frac{\pi}{7} \right)}} + \frac{5 \tan{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{14} \right)}}$$
/pi\ /5*pi\
- 5*sin|--| + 5*cos|----|
\14/ \ 14 /
-------------------------
/pi\ /pi\
cos|--|*sin|--|
\7 / \14/
$$\frac{- 5 \sin{\left(\frac{\pi}{14} \right)} + 5 \cos{\left(\frac{5 \pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)} \cos{\left(\frac{\pi}{7} \right)}}$$
/pi\ /5*pi\
5*csc|--|*csc|----|
/5*pi\ \14/ \ 14 /
- 5*csc|----| + -------------------
\ 14 / /pi\
csc|--|
\7 /
$$- 5 \csc{\left(\frac{5 \pi}{14} \right)} + \frac{5 \csc{\left(\frac{\pi}{14} \right)} \csc{\left(\frac{5 \pi}{14} \right)}}{\csc{\left(\frac{\pi}{7} \right)}}$$
/-3*pi\ /pi\
5*sec|-----|*sec|--|
/pi\ \ 7 / \7 /
- 5*sec|--| + --------------------
\7 / /-5*pi\
sec|-----|
\ 14 /
$$- 5 \sec{\left(\frac{\pi}{7} \right)} + \frac{5 \sec{\left(- \frac{3 \pi}{7} \right)} \sec{\left(\frac{\pi}{7} \right)}}{\sec{\left(- \frac{5 \pi}{14} \right)}}$$
2/pi\
10*sin |--|
5 \7 /
- ------- + -----------------
/pi\ /pi\ /2*pi\
cos|--| sin|--|*sin|----|
\7 / \14/ \ 7 /
$$- \frac{5}{\cos{\left(\frac{\pi}{7} \right)}} + \frac{10 \sin^{2}{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{14} \right)} \sin{\left(\frac{2 \pi}{7} \right)}}$$
/ /pi\ /pi\\
5*|- sin|--| + sin|--||
\ \14/ \7 //
-----------------------
/pi\ /5*pi\
sin|--|*sin|----|
\14/ \ 14 /
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \sin{\left(\frac{\pi}{7} \right)}\right)}{\sin{\left(\frac{\pi}{14} \right)} \sin{\left(\frac{5 \pi}{14} \right)}}$$
/-5*pi\
5*cos|-----|
5 \ 14 /
- ------- + ------------------
/pi\ /-3*pi\ /pi\
cos|--| cos|-----|*cos|--|
\7 / \ 7 / \7 /
$$- \frac{5}{\cos{\left(\frac{\pi}{7} \right)}} + \frac{5 \cos{\left(- \frac{5 \pi}{14} \right)}}{\cos{\left(- \frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}}$$
/ /pi\ /6*pi\\
5*|- sin|--| + sin|----||
\ \14/ \ 7 //
-------------------------
/pi\ /9*pi\
sin|--|*sin|----|
\14/ \ 14 /
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \sin{\left(\frac{6 \pi}{7} \right)}\right)}{\sin{\left(\frac{\pi}{14} \right)} \sin{\left(\frac{9 \pi}{14} \right)}}$$
/ /3*pi\ /5*pi\\
5*|- cos|----| + cos|----||
\ \ 7 / \ 14 //
---------------------------
/pi\ /3*pi\
cos|--|*cos|----|
\7 / \ 7 /
$$\frac{5 \left(- \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{5 \pi}{14} \right)}\right)}{\cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}}$$
2/pi\
10*sin |--|
5 \7 /
- --------- + -----------------
/9*pi\ /pi\ /2*pi\
sin|----| sin|--|*sin|----|
\ 14 / \14/ \ 7 /
$$- \frac{5}{\sin{\left(\frac{9 \pi}{14} \right)}} + \frac{10 \sin^{2}{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{14} \right)} \sin{\left(\frac{2 \pi}{7} \right)}}$$
/ /pi\ /pi\\
10*|- sin|--| + sin|--||
\ \14/ \7 //
------------------------
/3*pi\ /2*pi\
- cos|----| + cos|----|
\ 7 / \ 7 /
$$\frac{10 \left(- \sin{\left(\frac{\pi}{14} \right)} + \sin{\left(\frac{\pi}{7} \right)}\right)}{- \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{2 \pi}{7} \right)}}$$
/ /-3*pi\ /5*pi\\
5*|- cos|-----| + cos|----||
\ \ 7 / \ 14 //
----------------------------
/-3*pi\ /pi\
cos|-----|*cos|--|
\ 7 / \7 /
$$\frac{5 \left(- \cos{\left(- \frac{3 \pi}{7} \right)} + \cos{\left(\frac{5 \pi}{14} \right)}\right)}{\cos{\left(- \frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}}$$
/ /pi\ /pi\\
-10*|- sin|--| + sin|--||
\ \7 / \14//
-------------------------
/pi\ /3*pi\
- sin|--| + sin|----|
\14/ \ 14 /
$$- \frac{10 \left(- \sin{\left(\frac{\pi}{7} \right)} + \sin{\left(\frac{\pi}{14} \right)}\right)}{- \sin{\left(\frac{\pi}{14} \right)} + \sin{\left(\frac{3 \pi}{14} \right)}}$$
/ /13*pi\ /6*pi\\
5*|- sin|-----| + sin|----||
\ \ 14 / \ 7 //
----------------------------
/9*pi\ /13*pi\
sin|----|*sin|-----|
\ 14 / \ 14 /
$$\frac{5 \left(- \sin{\left(\frac{13 \pi}{14} \right)} + \sin{\left(\frac{6 \pi}{7} \right)}\right)}{\sin{\left(\frac{9 \pi}{14} \right)} \sin{\left(\frac{13 \pi}{14} \right)}}$$
/ /-3*pi\ /-5*pi\\
5*|- cos|-----| + cos|-----||
\ \ 7 / \ 14 //
-----------------------------
/-3*pi\ /-pi \
cos|-----|*cos|----|
\ 7 / \ 7 /
$$\frac{5 \left(- \cos{\left(- \frac{3 \pi}{7} \right)} + \cos{\left(- \frac{5 \pi}{14} \right)}\right)}{\cos{\left(- \frac{3 \pi}{7} \right)} \cos{\left(- \frac{\pi}{7} \right)}}$$
/ 1 1 \ /pi\ /5*pi\ 5*|------- - -------|*csc|--|*csc|----| | /pi\ /pi\| \14/ \ 14 / |csc|--| csc|--|| \ \7 / \14//
$$5 \left(- \frac{1}{\csc{\left(\frac{\pi}{14} \right)}} + \frac{1}{\csc{\left(\frac{\pi}{7} \right)}}\right) \csc{\left(\frac{\pi}{14} \right)} \csc{\left(\frac{5 \pi}{14} \right)}$$
/ 1 1 \ /pi\ /3*pi\ 5*|--------- - ---------|*sec|--|*sec|----| | /5*pi\ /3*pi\| \7 / \ 7 / |sec|----| sec|----|| \ \ 14 / \ 7 //
$$5 \left(- \frac{1}{\sec{\left(\frac{3 \pi}{7} \right)}} + \frac{1}{\sec{\left(\frac{5 \pi}{14} \right)}}\right) \sec{\left(\frac{\pi}{7} \right)} \sec{\left(\frac{3 \pi}{7} \right)}$$
/ 1 1 \ /-3*pi\ /pi\ 5*|--------- - ----------|*sec|-----|*sec|--| | /5*pi\ /-3*pi\| \ 7 / \7 / |sec|----| sec|-----|| \ \ 14 / \ 7 //
$$5 \left(- \frac{1}{\sec{\left(- \frac{3 \pi}{7} \right)}} + \frac{1}{\sec{\left(\frac{5 \pi}{14} \right)}}\right) \sec{\left(- \frac{3 \pi}{7} \right)} \sec{\left(\frac{\pi}{7} \right)}$$
/ 1 1 \ /5*pi\ /13*pi\ 5*|------- - ----------|*csc|----|*csc|-----| | /pi\ /13*pi\| \ 14 / \ 14 / |csc|--| csc|-----|| \ \7 / \ 14 //
$$5 \left(- \frac{1}{\csc{\left(\frac{13 \pi}{14} \right)}} + \frac{1}{\csc{\left(\frac{\pi}{7} \right)}}\right) \csc{\left(\frac{5 \pi}{14} \right)} \csc{\left(\frac{13 \pi}{14} \right)}$$
/ 2/pi\\ / 2/pi\\ /pi\
5*|1 + tan |--|| 5*|1 + tan |--||*tan|--|
\ \14// \ \28// \7 /
- ---------------- + ------------------------
2/pi\ /pi\
1 - tan |--| 2*tan|--|
\14/ \28/
$$- \frac{5 \left(\tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right)}{- \tan^{2}{\left(\frac{\pi}{14} \right)} + 1} + \frac{5 \left(\tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right) \tan{\left(\frac{\pi}{7} \right)}}{2 \tan{\left(\frac{\pi}{28} \right)}}$$
/ 1 /pi\\ /pi\
5*|------- + tan|--||*tan|--|
/ 2/pi\\ | /pi\ \28/| \7 /
5*|1 + tan |--|| |tan|--| |
\ \14// \ \28/ /
- ---------------- + -----------------------------
2/pi\ 2
1 - tan |--|
\14/
$$- \frac{5 \left(\tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right)}{- \tan^{2}{\left(\frac{\pi}{14} \right)} + 1} + \frac{5 \left(\tan{\left(\frac{\pi}{28} \right)} + \frac{1}{\tan{\left(\frac{\pi}{28} \right)}}\right) \tan{\left(\frac{\pi}{7} \right)}}{2}$$
/ /pi\ /pi\\
5*|- sin|--| + sin|--||
\ \7 / \14//
---------------------------------------
/ 2/pi\ 2/pi\\ /pi\ /pi\
2*|sin |--| - cos |--||*cos|--|*sin|--|
\ \14/ \14// \28/ \28/
$$\frac{5 \left(- \sin{\left(\frac{\pi}{7} \right)} + \sin{\left(\frac{\pi}{14} \right)}\right)}{2 \left(- \cos^{2}{\left(\frac{\pi}{14} \right)} + \sin^{2}{\left(\frac{\pi}{14} \right)}\right) \sin{\left(\frac{\pi}{28} \right)} \cos{\left(\frac{\pi}{28} \right)}}$$
/ 2/pi\\ / 2/pi\\
5*|1 + cot |--|| 5*|1 + cot |--||
\ \14// \ \28//
- ---------------- + -----------------
2/pi\ /pi\ /pi\
-1 + cot |--| 2*cot|--|*cot|--|
\14/ \7 / \28/
$$- \frac{5 \cdot \left(1 + \cot^{2}{\left(\frac{\pi}{14} \right)}\right)}{-1 + \cot^{2}{\left(\frac{\pi}{14} \right)}} + \frac{5 \cdot \left(1 + \cot^{2}{\left(\frac{\pi}{28} \right)}\right)}{2 \cot{\left(\frac{\pi}{28} \right)} \cot{\left(\frac{\pi}{7} \right)}}$$
/ /pi\ /pi\\ /pi\
-5*|- sin|--| + sin|--||*tan|--|
\ \7 / \14// \56/
----------------------------------
/ 2/pi\\ /pi\ 4/pi\
4*|-1 + cot |--||*cos|--|*sin |--|
\ \56// \7 / \56/
$$- \frac{5 \left(- \sin{\left(\frac{\pi}{7} \right)} + \sin{\left(\frac{\pi}{14} \right)}\right) \tan{\left(\frac{\pi}{56} \right)}}{4 \left(-1 + \cot^{2}{\left(\frac{\pi}{56} \right)}\right) \sin^{4}{\left(\frac{\pi}{56} \right)} \cos{\left(\frac{\pi}{7} \right)}}$$
/ /pi\ /pi\\
5*|- sin|--| + sin|--||
\ \7 / \14//
--------------------------------------------
/ 2/pi\ 2/4*pi\\ /pi\ /15*pi\
2*|sin |--| - sin |----||*sin|--|*sin|-----|
\ \14/ \ 7 // \28/ \ 28 /
$$\frac{5 \left(- \sin{\left(\frac{\pi}{7} \right)} + \sin{\left(\frac{\pi}{14} \right)}\right)}{2 \left(- \sin^{2}{\left(\frac{4 \pi}{7} \right)} + \sin^{2}{\left(\frac{\pi}{14} \right)}\right) \sin{\left(\frac{\pi}{28} \right)} \sin{\left(\frac{15 \pi}{28} \right)}}$$
/ 2/pi\\ / /pi\ /pi\\ /5*pi\
5*|1 + tan |--||*|- sin|--| + sin|--||*tan|----|
\ \28// \ \14/ \7 // \ 28 /
------------------------------------------------
2/5*pi\ /pi\
4*sin |----|*tan|--|
\ 28 / \28/
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \sin{\left(\frac{\pi}{7} \right)}\right) \left(\tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right) \tan{\left(\frac{5 \pi}{28} \right)}}{4 \sin^{2}{\left(\frac{5 \pi}{28} \right)} \tan{\left(\frac{\pi}{28} \right)}}$$
/ 2/9*pi\\ / /pi\ /pi\\ /pi\
5*|1 + cot |----||*|- sin|--| + sin|--||*tan|--|
\ \ 28 // \ \14/ \7 // \28/
------------------------------------------------
/9*pi\ 2/pi\
4*cot|----|*sin |--|
\ 28 / \28/
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \sin{\left(\frac{\pi}{7} \right)}\right) \left(\cot^{2}{\left(\frac{9 \pi}{28} \right)} + 1\right) \tan{\left(\frac{\pi}{28} \right)}}{4 \sin^{2}{\left(\frac{\pi}{28} \right)} \cot{\left(\frac{9 \pi}{28} \right)}}$$
/ 1 \ / /pi\ /pi\\
5*|-1 + -------|*|- sin|--| + sin|--||
| /pi\| \ \14/ \7 //
| cos|--||
\ \7 //
--------------------------------------
/pi\ 2/pi\ /pi\
4*cos|--|*sin |--|*sin|--|
\28/ \14/ \28/
$$\frac{5 \left(-1 + \frac{1}{\cos{\left(\frac{\pi}{7} \right)}}\right) \left(- \sin{\left(\frac{\pi}{14} \right)} + \sin{\left(\frac{\pi}{7} \right)}\right)}{4 \sin{\left(\frac{\pi}{28} \right)} \sin^{2}{\left(\frac{\pi}{14} \right)} \cos{\left(\frac{\pi}{28} \right)}}$$
/ 1 \ / /pi\ /pi\\ /pi\
5*|-1 + -------|*|- sin|--| + sin|--||*sec|--|
| /pi\| \ \14/ \7 // \28/
| cos|--||
\ \7 //
----------------------------------------------
2/pi\ /pi\
4*sin |--|*sin|--|
\14/ \28/
$$\frac{5 \left(-1 + \frac{1}{\cos{\left(\frac{\pi}{7} \right)}}\right) \left(- \sin{\left(\frac{\pi}{14} \right)} + \sin{\left(\frac{\pi}{7} \right)}\right) \sec{\left(\frac{\pi}{28} \right)}}{4 \sin{\left(\frac{\pi}{28} \right)} \sin^{2}{\left(\frac{\pi}{14} \right)}}$$
/ 1 \ / /pi\ /pi\\ /13*pi\
5*|-1 + -------|*|- sin|--| + sin|--||*csc|-----|
| /pi\| \ \14/ \7 // \ 28 /
| cos|--||
\ \7 //
-------------------------------------------------
2/pi\ /pi\
4*sin |--|*sin|--|
\14/ \28/
$$\frac{5 \left(-1 + \frac{1}{\cos{\left(\frac{\pi}{7} \right)}}\right) \left(- \sin{\left(\frac{\pi}{14} \right)} + \sin{\left(\frac{\pi}{7} \right)}\right) \csc{\left(\frac{13 \pi}{28} \right)}}{4 \sin{\left(\frac{\pi}{28} \right)} \sin^{2}{\left(\frac{\pi}{14} \right)}}$$
/ 1 \ / /pi\ /pi\\ /pi\
5*|-1 + -------|*|- sin|--| + sin|--||*tan|--|
| /pi\| \ \14/ \7 // \28/
| cos|--||
\ \7 //
----------------------------------------------
2/pi\ 2/pi\
4*sin |--|*sin |--|
\14/ \28/
$$\frac{5 \left(-1 + \frac{1}{\cos{\left(\frac{\pi}{7} \right)}}\right) \left(- \sin{\left(\frac{\pi}{14} \right)} + \sin{\left(\frac{\pi}{7} \right)}\right) \tan{\left(\frac{\pi}{28} \right)}}{4 \sin^{2}{\left(\frac{\pi}{28} \right)} \sin^{2}{\left(\frac{\pi}{14} \right)}}$$
/ /-5*pi\ /-3*pi\\
5*|- cos|-----| + cos|-----||
\ \ 14 / \ 7 //
----------------------------------------------
/ 2/-3*pi\ 2/pi\\ /-13*pi\ /pi\
2*|cos |-----| - cos |--||*cos|------|*cos|--|
\ \ 7 / \14// \ 28 / \28/
$$\frac{5 \left(- \cos{\left(- \frac{5 \pi}{14} \right)} + \cos{\left(- \frac{3 \pi}{7} \right)}\right)}{2 \left(- \cos^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(- \frac{3 \pi}{7} \right)}\right) \cos{\left(- \frac{13 \pi}{28} \right)} \cos{\left(\frac{\pi}{28} \right)}}$$
/ 2/pi\\ / 2/5*pi\\ / /pi\ /pi\\
5*|1 + tan |--||*|1 + tan |----||*|- sin|--| + sin|--||
\ \28// \ \ 28 // \ \14/ \7 //
-------------------------------------------------------
/pi\ /5*pi\
4*tan|--|*tan|----|
\28/ \ 28 /
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \sin{\left(\frac{\pi}{7} \right)}\right) \left(\tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right) \left(\tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1\right)}{4 \tan{\left(\frac{\pi}{28} \right)} \tan{\left(\frac{5 \pi}{28} \right)}}$$
/ /pi\ /pi\\
5*|- sin|--| + sin|--||
\ \14/ \7 //
-----------------------------------------------------
/ 2/pi\\ / 2/3*pi\\ 2/pi\ 2/3*pi\
|-1 + cot |--||*|-1 + cot |----||*sin |--|*sin |----|
\ \14// \ \ 14 // \14/ \ 14 /
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \sin{\left(\frac{\pi}{7} \right)}\right)}{\left(-1 + \cot^{2}{\left(\frac{\pi}{14} \right)}\right) \left(-1 + \cot^{2}{\left(\frac{3 \pi}{14} \right)}\right) \sin^{2}{\left(\frac{\pi}{14} \right)} \sin^{2}{\left(\frac{3 \pi}{14} \right)}}$$
/ 1 1 \ /pi\ /13*pi\
5*|------- - -------|*csc|--|*csc|-----|
| /pi\ /pi\| \28/ \ 28 /
|csc|--| csc|--||
\ \14/ \7 //
----------------------------------------
/ 1 1 \
2*|-------- - ----------|
| 2/pi\ 2/3*pi\|
|csc |--| csc |----||
\ \14/ \ 7 //
$$\frac{5 \left(- \frac{1}{\csc{\left(\frac{\pi}{7} \right)}} + \frac{1}{\csc{\left(\frac{\pi}{14} \right)}}\right) \csc{\left(\frac{\pi}{28} \right)} \csc{\left(\frac{13 \pi}{28} \right)}}{2 \left(- \frac{1}{\csc^{2}{\left(\frac{3 \pi}{7} \right)}} + \frac{1}{\csc^{2}{\left(\frac{\pi}{14} \right)}}\right)}$$
/ 1 1 \ /-13*pi\ /pi\
5*|---------- - ----------|*sec|------|*sec|--|
| /-3*pi\ /-5*pi\| \ 28 / \28/
|sec|-----| sec|-----||
\ \ 7 / \ 14 //
-----------------------------------------------
/ 1 1 \
2*|----------- - --------|
| 2/-3*pi\ 2/pi\|
|sec |-----| sec |--||
\ \ 7 / \14//
$$\frac{5 \left(- \frac{1}{\sec{\left(- \frac{5 \pi}{14} \right)}} + \frac{1}{\sec{\left(- \frac{3 \pi}{7} \right)}}\right) \sec{\left(- \frac{13 \pi}{28} \right)} \sec{\left(\frac{\pi}{28} \right)}}{2 \left(- \frac{1}{\sec^{2}{\left(\frac{\pi}{14} \right)}} + \frac{1}{\sec^{2}{\left(- \frac{3 \pi}{7} \right)}}\right)}$$
/ 2/5*pi\\
| 1 - tan |----||
/ 2/pi\\ / 2/pi\\ | /pi\ \ 28 /|
5*|1 + tan |--||*|1 + tan |--||*|- sin|--| + --------------|
\ \14// \ \28// | \14/ 2/5*pi\|
| 1 + tan |----||
\ \ 28 //
------------------------------------------------------------
/ 2/pi\\ /pi\
2*|1 - tan |--||*tan|--|
\ \14// \28/
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \frac{- \tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1}{\tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right)}{2 \cdot \left(- \tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right) \tan{\left(\frac{\pi}{28} \right)}}$$
/ 2/5*pi\\
| 1 - tan |----||
/ 2/pi\\ / 2/pi\\ | /pi\ \ 28 /| /pi\
5*|1 + tan |--||*|1 + tan |--||*|- sin|--| + --------------|*cot|--|
\ \14// \ \28// | \14/ 2/5*pi\| \28/
| 1 + tan |----||
\ \ 28 //
--------------------------------------------------------------------
/ 2/pi\\
2*|1 - tan |--||
\ \14//
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \frac{- \tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1}{\tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right) \cot{\left(\frac{\pi}{28} \right)}}{2 \cdot \left(- \tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right)}$$
/ /pi\ /pi\ \
| 2*tan|--| 2*tan|--| |
/ 2/pi\\ / 2/5*pi\\ | \28/ \14/ |
5*|1 + tan |--||*|1 + tan |----||*|- ------------ + ------------|
\ \28// \ \ 28 // | 2/pi\ 2/pi\|
| 1 + tan |--| 1 + tan |--||
\ \28/ \14//
-----------------------------------------------------------------
/pi\ /5*pi\
4*tan|--|*tan|----|
\28/ \ 28 /
$$\frac{5 \left(- \frac{2 \tan{\left(\frac{\pi}{28} \right)}}{\tan^{2}{\left(\frac{\pi}{28} \right)} + 1} + \frac{2 \tan{\left(\frac{\pi}{14} \right)}}{\tan^{2}{\left(\frac{\pi}{14} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right) \left(\tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1\right)}{4 \tan{\left(\frac{\pi}{28} \right)} \tan{\left(\frac{5 \pi}{28} \right)}}$$
/ /pi\ /pi\ \
| 2*cot|--| 2*cot|--| |
/ 2/pi\\ / 2/5*pi\\ | \28/ \14/ |
5*|1 + cot |--||*|1 + cot |----||*|- ------------ + ------------|
\ \28// \ \ 28 // | 2/pi\ 2/pi\|
| 1 + cot |--| 1 + cot |--||
\ \28/ \14//
-----------------------------------------------------------------
/pi\ /5*pi\
4*cot|--|*cot|----|
\28/ \ 28 /
$$\frac{5 \cdot \left(1 + \cot^{2}{\left(\frac{\pi}{28} \right)}\right) \left(1 + \cot^{2}{\left(\frac{5 \pi}{28} \right)}\right) \left(- \frac{2 \cot{\left(\frac{\pi}{28} \right)}}{1 + \cot^{2}{\left(\frac{\pi}{28} \right)}} + \frac{2 \cot{\left(\frac{\pi}{14} \right)}}{1 + \cot^{2}{\left(\frac{\pi}{14} \right)}}\right)}{4 \cot{\left(\frac{\pi}{28} \right)} \cot{\left(\frac{5 \pi}{28} \right)}}$$
/ /pi\ /3*pi\ \
| 2*tan|--| 2*tan|----| |
/ 2/pi\\ / 2/9*pi\\ | \28/ \ 7 / |
5*|1 + tan |--||*|1 + tan |----||*|- ------------ + --------------|
\ \28// \ \ 28 // | 2/pi\ 2/3*pi\|
| 1 + tan |--| 1 + tan |----||
\ \28/ \ 7 //
-------------------------------------------------------------------
/pi\ /9*pi\
4*tan|--|*tan|----|
\28/ \ 28 /
$$\frac{5 \cdot \left(1 + \tan^{2}{\left(\frac{9 \pi}{28} \right)}\right) \left(- \frac{2 \tan{\left(\frac{\pi}{28} \right)}}{\tan^{2}{\left(\frac{\pi}{28} \right)} + 1} + \frac{2 \tan{\left(\frac{3 \pi}{7} \right)}}{1 + \tan^{2}{\left(\frac{3 \pi}{7} \right)}}\right) \left(\tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right)}{4 \tan{\left(\frac{\pi}{28} \right)} \tan{\left(\frac{9 \pi}{28} \right)}}$$
/ /pi\ /3*pi\ \
| 2*cot|--| 2*cot|----| |
/ 2/pi\\ / 2/9*pi\\ | \28/ \ 7 / |
5*|1 + cot |--||*|1 + cot |----||*|- ------------ + --------------|
\ \28// \ \ 28 // | 2/pi\ 2/3*pi\|
| 1 + cot |--| 1 + cot |----||
\ \28/ \ 7 //
-------------------------------------------------------------------
/pi\ /9*pi\
4*cot|--|*cot|----|
\28/ \ 28 /
$$\frac{5 \cdot \left(1 + \cot^{2}{\left(\frac{\pi}{28} \right)}\right) \left(- \frac{2 \cot{\left(\frac{\pi}{28} \right)}}{1 + \cot^{2}{\left(\frac{\pi}{28} \right)}} + \frac{2 \cot{\left(\frac{3 \pi}{7} \right)}}{\cot^{2}{\left(\frac{3 \pi}{7} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{9 \pi}{28} \right)} + 1\right)}{4 \cot{\left(\frac{\pi}{28} \right)} \cot{\left(\frac{9 \pi}{28} \right)}}$$
/ 2/5*pi\\
| 1 - tan |----||
/ 2/pi\\ / 2/pi\\ | /pi\ \ 28 /| /pi\
5*|1 + tan |--||*|1 + tan |--||*|- sin|--| + --------------|*cos|--|
\ \14// \ \28// | \14/ 2/5*pi\| \28/
| 1 + tan |----||
\ \ 28 //
--------------------------------------------------------------------
/ 2/pi\\ /pi\
2*|1 - tan |--||*sin|--|
\ \14// \28/
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \frac{- \tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1}{\tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right) \cos{\left(\frac{\pi}{28} \right)}}{2 \cdot \left(- \tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right) \sin{\left(\frac{\pi}{28} \right)}}$$
/ 2/5*pi\\
| 1 - tan |----||
/ 2/pi\\ / 2/pi\\ | /pi\ \ 28 /| /pi\ /pi\
5*|1 + tan |--||*|1 + tan |--||*|- sin|--| + --------------|*cos|--|*csc|--|
\ \14// \ \28// | \14/ 2/5*pi\| \28/ \28/
| 1 + tan |----||
\ \ 28 //
----------------------------------------------------------------------------
/ 2/pi\\
2*|1 - tan |--||
\ \14//
$$\frac{5 \left(- \sin{\left(\frac{\pi}{14} \right)} + \frac{- \tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1}{\tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right) \cos{\left(\frac{\pi}{28} \right)} \csc{\left(\frac{\pi}{28} \right)}}{2 \cdot \left(- \tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right)}$$
2 2 / 2/pi\\ / 2/pi\\ / /pi\ /pi\\ 5*|1 + tan |--|| *|1 + tan |--|| *|- sin|--| + sin|--|| \ \28// \ \56// \ \7 / \14// ------------------------------------------------------- / 2/pi\\ / 4/pi\ 2/pi\\ /pi\ 4*|1 - tan |--||*|-1 - tan |--| + 6*tan |--||*tan|--| \ \56// \ \28/ \28// \56/
$$\frac{5 \left(- \sin{\left(\frac{\pi}{7} \right)} + \sin{\left(\frac{\pi}{14} \right)}\right) \left(\tan^{2}{\left(\frac{\pi}{56} \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right)^{2}}{4 \cdot \left(- \tan^{2}{\left(\frac{\pi}{56} \right)} + 1\right) \left(-1 - \tan^{4}{\left(\frac{\pi}{28} \right)} + 6 \tan^{2}{\left(\frac{\pi}{28} \right)}\right) \tan{\left(\frac{\pi}{56} \right)}}$$
/ 2/5*pi\ /pi\ \
|-1 + cot |----| 2*cot|--| |
/ 2/pi\\ / 2/pi\\ | \ 28 / \28/ |
5*|1 + cot |--||*|1 + cot |--||*|--------------- - ------------|
\ \14// \ \28// | 2/5*pi\ 2/pi\|
| 1 + cot |----| 1 + cot |--||
\ \ 28 / \28//
----------------------------------------------------------------
/ 2/pi\\ /pi\
2*|-1 + cot |--||*cot|--|
\ \14// \28/
$$\frac{5 \cdot \left(1 + \cot^{2}{\left(\frac{\pi}{28} \right)}\right) \left(1 + \cot^{2}{\left(\frac{\pi}{14} \right)}\right) \left(- \frac{2 \cot{\left(\frac{\pi}{28} \right)}}{1 + \cot^{2}{\left(\frac{\pi}{28} \right)}} + \frac{-1 + \cot^{2}{\left(\frac{5 \pi}{28} \right)}}{1 + \cot^{2}{\left(\frac{5 \pi}{28} \right)}}\right)}{2 \left(-1 + \cot^{2}{\left(\frac{\pi}{14} \right)}\right) \cot{\left(\frac{\pi}{28} \right)}}$$
/ 2/5*pi\ /pi\ \
|1 - tan |----| 2*tan|--| |
/ 2/pi\\ / 2/pi\\ | \ 28 / \28/ |
5*|1 + tan |--||*|1 + tan |--||*|-------------- - ------------|
\ \14// \ \28// | 2/5*pi\ 2/pi\|
|1 + tan |----| 1 + tan |--||
\ \ 28 / \28//
---------------------------------------------------------------
/ 2/pi\\ /pi\
2*|1 - tan |--||*tan|--|
\ \14// \28/
$$\frac{5 \left(- \frac{2 \tan{\left(\frac{\pi}{28} \right)}}{\tan^{2}{\left(\frac{\pi}{28} \right)} + 1} + \frac{- \tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1}{\tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right)}{2 \cdot \left(- \tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right) \tan{\left(\frac{\pi}{28} \right)}}$$
/ 2/5*pi\ 2/3*pi\\
|1 - tan |----| 1 - tan |----||
/ 2/pi\\ / 2/3*pi\\ | \ 28 / \ 14 /|
5*|1 + tan |--||*|1 + tan |----||*|-------------- - --------------|
\ \14// \ \ 14 // | 2/5*pi\ 2/3*pi\|
|1 + tan |----| 1 + tan |----||
\ \ 28 / \ 14 //
-------------------------------------------------------------------
/ 2/pi\\ / 2/3*pi\\
|1 - tan |--||*|1 - tan |----||
\ \14// \ \ 14 //
$$\frac{5 \left(- \frac{- \tan^{2}{\left(\frac{3 \pi}{14} \right)} + 1}{\tan^{2}{\left(\frac{3 \pi}{14} \right)} + 1} + \frac{- \tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1}{\tan^{2}{\left(\frac{5 \pi}{28} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right) \left(\tan^{2}{\left(\frac{3 \pi}{14} \right)} + 1\right)}{\left(- \tan^{2}{\left(\frac{\pi}{14} \right)} + 1\right) \left(- \tan^{2}{\left(\frac{3 \pi}{14} \right)} + 1\right)}$$
/ 2/5*pi\ 2/3*pi\\
|-1 + cot |----| -1 + cot |----||
/ 2/pi\\ / 2/3*pi\\ | \ 28 / \ 14 /|
5*|1 + cot |--||*|1 + cot |----||*|--------------- - ---------------|
\ \14// \ \ 14 // | 2/5*pi\ 2/3*pi\|
| 1 + cot |----| 1 + cot |----||
\ \ 28 / \ 14 //
---------------------------------------------------------------------
/ 2/pi\\ / 2/3*pi\\
|-1 + cot |--||*|-1 + cot |----||
\ \14// \ \ 14 //
$$\frac{5 \cdot \left(1 + \cot^{2}{\left(\frac{\pi}{14} \right)}\right) \left(1 + \cot^{2}{\left(\frac{3 \pi}{14} \right)}\right) \left(- \frac{-1 + \cot^{2}{\left(\frac{3 \pi}{14} \right)}}{1 + \cot^{2}{\left(\frac{3 \pi}{14} \right)}} + \frac{-1 + \cot^{2}{\left(\frac{5 \pi}{28} \right)}}{1 + \cot^{2}{\left(\frac{5 \pi}{28} \right)}}\right)}{\left(-1 + \cot^{2}{\left(\frac{\pi}{14} \right)}\right) \left(-1 + \cot^{2}{\left(\frac{3 \pi}{14} \right)}\right)}$$
/ 1 \
|1 - ---------- |
| 2/5*pi\ /pi\ |
| cot |----| 2*cot|--| |
/ 1 \ / 1 \ | \ 28 / \28/ | /pi\
5*|1 + --------|*|1 + --------|*|-------------- - ------------|*cot|--|
| 2/pi\| | 2/pi\| | 1 2/pi\| \28/
| cot |--|| | cot |--|| |1 + ---------- 1 + cot |--||
\ \14// \ \28// | 2/5*pi\ \28/|
| cot |----| |
\ \ 28 / /
-----------------------------------------------------------------------
/ 1 \
2*|1 - --------|
| 2/pi\|
| cot |--||
\ \14//
$$\frac{5 \left(- \frac{2 \cot{\left(\frac{\pi}{28} \right)}}{1 + \cot^{2}{\left(\frac{\pi}{28} \right)}} + \frac{- \frac{1}{\cot^{2}{\left(\frac{5 \pi}{28} \right)}} + 1}{\frac{1}{\cot^{2}{\left(\frac{5 \pi}{28} \right)}} + 1}\right) \left(\frac{1}{\cot^{2}{\left(\frac{\pi}{28} \right)}} + 1\right) \left(\frac{1}{\cot^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \cot{\left(\frac{\pi}{28} \right)}}{2 \cdot \left(- \frac{1}{\cot^{2}{\left(\frac{\pi}{14} \right)}} + 1\right)}$$
/ 1 \
|-1 + ---------- |
| 2/5*pi\ |
| tan |----| |
/ 1 \ / 1 \ | \ 28 / 2 | /pi\
5*|1 + --------|*|1 + --------|*|--------------- - ----------------------|*tan|--|
| 2/pi\| | 2/pi\| | 1 / 1 \ /pi\| \28/
| tan |--|| | tan |--|| | 1 + ---------- |1 + --------|*tan|--||
\ \14// \ \28// | 2/5*pi\ | 2/pi\| \28/|
| tan |----| | tan |--|| |
\ \ 28 / \ \28// /
----------------------------------------------------------------------------------
/ 1 \
2*|-1 + --------|
| 2/pi\|
| tan |--||
\ \14//
$$\frac{5 \cdot \left(1 + \frac{1}{\tan^{2}{\left(\frac{\pi}{28} \right)}}\right) \left(1 + \frac{1}{\tan^{2}{\left(\frac{\pi}{14} \right)}}\right) \left(- \frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{\pi}{28} \right)}}\right) \tan{\left(\frac{\pi}{28} \right)}} + \frac{-1 + \frac{1}{\tan^{2}{\left(\frac{5 \pi}{28} \right)}}}{1 + \frac{1}{\tan^{2}{\left(\frac{5 \pi}{28} \right)}}}\right) \tan{\left(\frac{\pi}{28} \right)}}{2 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{\pi}{14} \right)}}\right)}$$
/ 1 \
|1 - ---------- |
| 2/5*pi\ |
| cot |----| |
/ 1 \ / 1 \ | \ 28 / 2 | /pi\
5*|1 + --------|*|1 + --------|*|-------------- - ----------------------|*cot|--|
| 2/pi\| | 2/pi\| | 1 / 1 \ /pi\| \28/
| cot |--|| | cot |--|| |1 + ---------- |1 + --------|*cot|--||
\ \14// \ \28// | 2/5*pi\ | 2/pi\| \28/|
| cot |----| | cot |--|| |
\ \ 28 / \ \28// /
---------------------------------------------------------------------------------
/ 1 \
2*|1 - --------|
| 2/pi\|
| cot |--||
\ \14//
$$\frac{5 \left(- \frac{2}{\left(\frac{1}{\cot^{2}{\left(\frac{\pi}{28} \right)}} + 1\right) \cot{\left(\frac{\pi}{28} \right)}} + \frac{- \frac{1}{\cot^{2}{\left(\frac{5 \pi}{28} \right)}} + 1}{\frac{1}{\cot^{2}{\left(\frac{5 \pi}{28} \right)}} + 1}\right) \left(\frac{1}{\cot^{2}{\left(\frac{\pi}{28} \right)}} + 1\right) \left(\frac{1}{\cot^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \cot{\left(\frac{\pi}{28} \right)}}{2 \cdot \left(- \frac{1}{\cot^{2}{\left(\frac{\pi}{14} \right)}} + 1\right)}$$
/ /pi\ /pi\ \
2 | 2*cot|--| 2*cot|--| |
/ 2/pi\\ | \14/ \28/ |
5*|1 + cot |--|| *|- ------------ + ------------|
\ \56// | 2/pi\ 2/pi\|
| 1 + cot |--| 1 + cot |--||
\ \14/ \28//
----------------------------------------------------------------
/ 2 \
| / 2/pi\\ 2/pi\ |
| |-1 + cot |--|| 4*cot |--| |
/ 2/pi\\ | \ \28// \28/ | /pi\
4*|-1 + cot |--||*|- ---------------- + ---------------|*cot|--|
\ \56// | 2 2| \56/
| / 2/pi\\ / 2/pi\\ |
| |1 + cot |--|| |1 + cot |--|| |
\ \ \28// \ \28// /
$$\frac{5 \left(1 + \cot^{2}{\left(\frac{\pi}{56} \right)}\right)^{2} \left(- \frac{2 \cot{\left(\frac{\pi}{14} \right)}}{1 + \cot^{2}{\left(\frac{\pi}{14} \right)}} + \frac{2 \cot{\left(\frac{\pi}{28} \right)}}{1 + \cot^{2}{\left(\frac{\pi}{28} \right)}}\right)}{4 \left(-1 + \cot^{2}{\left(\frac{\pi}{56} \right)}\right) \left(- \frac{\left(-1 + \cot^{2}{\left(\frac{\pi}{28} \right)}\right)^{2}}{\left(1 + \cot^{2}{\left(\frac{\pi}{28} \right)}\right)^{2}} + \frac{4 \cot^{2}{\left(\frac{\pi}{28} \right)}}{\left(1 + \cot^{2}{\left(\frac{\pi}{28} \right)}\right)^{2}}\right) \cot{\left(\frac{\pi}{56} \right)}}$$
/ /pi\ /pi\ \
2 | 2*tan|--| 2*tan|--| |
/ 2/pi\\ | \14/ \28/ |
5*|1 + tan |--|| *|- ------------ + ------------|
\ \56// | 2/pi\ 2/pi\|
| 1 + tan |--| 1 + tan |--||
\ \14/ \28//
--------------------------------------------------------------
/ 2 \
| / 2/pi\\ 2/pi\ |
| |1 - tan |--|| 4*tan |--| |
/ 2/pi\\ | \ \28// \28/ | /pi\
4*|1 - tan |--||*|- --------------- + ---------------|*tan|--|
\ \56// | 2 2| \56/
| / 2/pi\\ / 2/pi\\ |
| |1 + tan |--|| |1 + tan |--|| |
\ \ \28// \ \28// /
$$\frac{5 \left(- \frac{2 \tan{\left(\frac{\pi}{14} \right)}}{\tan^{2}{\left(\frac{\pi}{14} \right)} + 1} + \frac{2 \tan{\left(\frac{\pi}{28} \right)}}{\tan^{2}{\left(\frac{\pi}{28} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{\pi}{56} \right)} + 1\right)^{2}}{4 \cdot \left(- \tan^{2}{\left(\frac{\pi}{56} \right)} + 1\right) \left(- \frac{\left(- \tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(\frac{\pi}{28} \right)}}{\left(\tan^{2}{\left(\frac{\pi}{28} \right)} + 1\right)^{2}}\right) \tan{\left(\frac{\pi}{56} \right)}}$$
/ 4/5*pi\\
| 4*sin |----||
| \ 28 /|
| 1 - ------------|
/ 4/pi\\ / 4/pi\\ | 2/pi\ |
| 4*sin |--|| | 4*sin |--|| | cos |--| |
| \14/| | \28/| | /pi\ \7 / | /pi\
5*|1 + ----------|*|1 + ----------|*|- sin|--| + ----------------|*sin|--|
| 2/pi\ | | 2/pi\ | | \14/ 4/5*pi\| \14/
| sin |--| | | sin |--| | | 4*sin |----||
\ \7 / / \ \14/ / | \ 28 /|
| 1 + ------------|
| 2/pi\ |
| cos |--| |
\ \7 / /
--------------------------------------------------------------------------
/ 4/pi\\
| 4*sin |--||
| \14/| 2/pi\
4*|1 - ----------|*sin |--|
| 2/pi\ | \28/
| sin |--| |
\ \7 / /
$$\frac{5 \cdot \left(\frac{4 \sin^{4}{\left(\frac{\pi}{28} \right)}}{\sin^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \left(\frac{4 \sin^{4}{\left(\frac{\pi}{14} \right)}}{\sin^{2}{\left(\frac{\pi}{7} \right)}} + 1\right) \left(- \sin{\left(\frac{\pi}{14} \right)} + \frac{- \frac{4 \sin^{4}{\left(\frac{5 \pi}{28} \right)}}{\cos^{2}{\left(\frac{\pi}{7} \right)}} + 1}{\frac{4 \sin^{4}{\left(\frac{5 \pi}{28} \right)}}{\cos^{2}{\left(\frac{\pi}{7} \right)}} + 1}\right) \sin{\left(\frac{\pi}{14} \right)}}{4 \left(- \frac{4 \sin^{4}{\left(\frac{\pi}{14} \right)}}{\sin^{2}{\left(\frac{\pi}{7} \right)}} + 1\right) \sin^{2}{\left(\frac{\pi}{28} \right)}}$$
/ 4/5*pi\\
| 4*sin |----||
| \ 28 /|
| 1 - ------------|
/ 4/pi\\ / 4/pi\\ | 2/5*pi\ |
| 4*sin |--|| | 4*sin |--|| | sin |----| |
| \14/| | \28/| | /pi\ \ 14 / | /pi\
5*|1 + ----------|*|1 + ----------|*|- sin|--| + ----------------|*sin|--|
| 2/pi\ | | 2/pi\ | | \14/ 4/5*pi\| \14/
| sin |--| | | sin |--| | | 4*sin |----||
\ \7 / / \ \14/ / | \ 28 /|
| 1 + ------------|
| 2/5*pi\ |
| sin |----| |
\ \ 14 / /
--------------------------------------------------------------------------
/ 4/pi\\
| 4*sin |--||
| \14/| 2/pi\
4*|1 - ----------|*sin |--|
| 2/pi\ | \28/
| sin |--| |
\ \7 / /
$$\frac{5 \cdot \left(\frac{4 \sin^{4}{\left(\frac{\pi}{28} \right)}}{\sin^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \left(\frac{4 \sin^{4}{\left(\frac{\pi}{14} \right)}}{\sin^{2}{\left(\frac{\pi}{7} \right)}} + 1\right) \left(- \sin{\left(\frac{\pi}{14} \right)} + \frac{- \frac{4 \sin^{4}{\left(\frac{5 \pi}{28} \right)}}{\sin^{2}{\left(\frac{5 \pi}{14} \right)}} + 1}{\frac{4 \sin^{4}{\left(\frac{5 \pi}{28} \right)}}{\sin^{2}{\left(\frac{5 \pi}{14} \right)}} + 1}\right) \sin{\left(\frac{\pi}{14} \right)}}{4 \left(- \frac{4 \sin^{4}{\left(\frac{\pi}{14} \right)}}{\sin^{2}{\left(\frac{\pi}{7} \right)}} + 1\right) \sin^{2}{\left(\frac{\pi}{28} \right)}}$$
/ 2/9*pi\\
| csc |----||
| \ 28 /|
| 1 - ----------|
/ 2/3*pi\\ / 2/13*pi\\ | 2/5*pi\|
| csc |----|| | csc |-----|| | csc |----||
| \ 7 /| | \ 28 /| | 1 \ 28 /| /pi\
5*|1 + ----------|*|1 + -----------|*|- ------- + --------------|*csc|--|
| 2/pi\ | | 2/pi\ | | /pi\ 2/9*pi\| \28/
| csc |--| | | csc |--| | | csc|--| csc |----||
\ \14/ / \ \28/ / | \14/ \ 28 /|
| 1 + ----------|
| 2/5*pi\|
| csc |----||
\ \ 28 //
-------------------------------------------------------------------------
/ 2/3*pi\\
| csc |----||
| \ 7 /| /13*pi\
2*|1 - ----------|*csc|-----|
| 2/pi\ | \ 28 /
| csc |--| |
\ \14/ /
$$\frac{5 \left(\frac{\csc^{2}{\left(\frac{13 \pi}{28} \right)}}{\csc^{2}{\left(\frac{\pi}{28} \right)}} + 1\right) \left(\frac{\csc^{2}{\left(\frac{3 \pi}{7} \right)}}{\csc^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \left(- \frac{1}{\csc{\left(\frac{\pi}{14} \right)}} + \frac{- \frac{\csc^{2}{\left(\frac{9 \pi}{28} \right)}}{\csc^{2}{\left(\frac{5 \pi}{28} \right)}} + 1}{\frac{\csc^{2}{\left(\frac{9 \pi}{28} \right)}}{\csc^{2}{\left(\frac{5 \pi}{28} \right)}} + 1}\right) \csc{\left(\frac{\pi}{28} \right)}}{2 \left(- \frac{\csc^{2}{\left(\frac{3 \pi}{7} \right)}}{\csc^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \csc{\left(\frac{13 \pi}{28} \right)}}$$
/ 2/-9*pi\\
| cos |-----||
| \ 28 /|
| 1 - -----------|
/ 2/-13*pi\\ / 2/-3*pi\\ | 2/5*pi\|
| cos |------|| | cos |-----|| | cos |----||
| \ 28 /| | \ 7 /| | /-3*pi\ \ 28 /| /pi\
5*|1 + ------------|*|1 + -----------|*|- cos|-----| + ---------------|*cos|--|
| 2/pi\ | | 2/pi\ | | \ 7 / 2/-9*pi\| \28/
| cos |--| | | cos |--| | | cos |-----||
\ \28/ / \ \14/ / | \ 28 /|
| 1 + -----------|
| 2/5*pi\|
| cos |----||
\ \ 28 //
-------------------------------------------------------------------------------
/ 2/-3*pi\\
| cos |-----||
| \ 7 /| /-13*pi\
2*|1 - -----------|*cos|------|
| 2/pi\ | \ 28 /
| cos |--| |
\ \14/ /
$$\frac{5 \left(\frac{\cos^{2}{\left(- \frac{13 \pi}{28} \right)}}{\cos^{2}{\left(\frac{\pi}{28} \right)}} + 1\right) \left(\frac{\cos^{2}{\left(- \frac{3 \pi}{7} \right)}}{\cos^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \left(- \cos{\left(- \frac{3 \pi}{7} \right)} + \frac{- \frac{\cos^{2}{\left(- \frac{9 \pi}{28} \right)}}{\cos^{2}{\left(\frac{5 \pi}{28} \right)}} + 1}{\frac{\cos^{2}{\left(- \frac{9 \pi}{28} \right)}}{\cos^{2}{\left(\frac{5 \pi}{28} \right)}} + 1}\right) \cos{\left(\frac{\pi}{28} \right)}}{2 \left(- \frac{\cos^{2}{\left(- \frac{3 \pi}{7} \right)}}{\cos^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \cos{\left(- \frac{13 \pi}{28} \right)}}$$
/ 2/5*pi\\
| sec |----||
| \ 28 /|
| 1 - -----------|
/ 2/pi\ \ / 2/pi\ \ | 2/-9*pi\|
| sec |--| | | sec |--| | | sec |-----||
| \28/ | | \14/ | | 1 \ 28 /| /-13*pi\
5*|1 + ------------|*|1 + -----------|*|- ---------- + ---------------|*sec|------|
| 2/-13*pi\| | 2/-3*pi\| | /-3*pi\ 2/5*pi\| \ 28 /
| sec |------|| | sec |-----|| | sec|-----| sec |----||
\ \ 28 // \ \ 7 // | \ 7 / \ 28 /|
| 1 + -----------|
| 2/-9*pi\|
| sec |-----||
\ \ 28 //
-----------------------------------------------------------------------------------
/ 2/pi\ \
| sec |--| |
| \14/ | /pi\
2*|1 - -----------|*sec|--|
| 2/-3*pi\| \28/
| sec |-----||
\ \ 7 //
$$\frac{5 \left(\frac{\sec^{2}{\left(\frac{\pi}{28} \right)}}{\sec^{2}{\left(- \frac{13 \pi}{28} \right)}} + 1\right) \left(\frac{\sec^{2}{\left(\frac{\pi}{14} \right)}}{\sec^{2}{\left(- \frac{3 \pi}{7} \right)}} + 1\right) \left(- \frac{1}{\sec{\left(- \frac{3 \pi}{7} \right)}} + \frac{- \frac{\sec^{2}{\left(\frac{5 \pi}{28} \right)}}{\sec^{2}{\left(- \frac{9 \pi}{28} \right)}} + 1}{\frac{\sec^{2}{\left(\frac{5 \pi}{28} \right)}}{\sec^{2}{\left(- \frac{9 \pi}{28} \right)}} + 1}\right) \sec{\left(- \frac{13 \pi}{28} \right)}}{2 \left(- \frac{\sec^{2}{\left(\frac{\pi}{14} \right)}}{\sec^{2}{\left(- \frac{3 \pi}{7} \right)}} + 1\right) \sec{\left(\frac{\pi}{28} \right)}}$$
/ 4/5*pi\ \
| 4*sin |----| |
| \ 28 / |
|1 - ------------ |
/ 4/pi\\ / 4/pi\\ | 2/pi\ /pi\ |
| 4*sin |--|| | 4*sin |--|| | cos |--| 4*sin|--| |
| \14/| | \28/| | \7 / \14/ | /pi\
5*|1 + ----------|*|1 + ----------|*|---------------- - ---------------------|*sin|--|
| 2/pi\ | | 2/pi\ | | 4/5*pi\ 2/pi\| \14/
| sin |--| | | sin |--| | | 4*sin |----| sin |--||
\ \7 / / \ \14/ / | \ 28 / 2/pi\ \14/|
|1 + ------------ 4*sin |--| + --------|
| 2/pi\ \28/ 2/pi\|
| cos |--| sin |--||
\ \7 / \28//
--------------------------------------------------------------------------------------
/ 4/pi\\
| 4*sin |--||
| \14/| 2/pi\
4*|1 - ----------|*sin |--|
| 2/pi\ | \28/
| sin |--| |
\ \7 / /
$$\frac{5 \left(- \frac{4 \sin{\left(\frac{\pi}{14} \right)}}{4 \sin^{2}{\left(\frac{\pi}{28} \right)} + \frac{\sin^{2}{\left(\frac{\pi}{14} \right)}}{\sin^{2}{\left(\frac{\pi}{28} \right)}}} + \frac{- \frac{4 \sin^{4}{\left(\frac{5 \pi}{28} \right)}}{\cos^{2}{\left(\frac{\pi}{7} \right)}} + 1}{\frac{4 \sin^{4}{\left(\frac{5 \pi}{28} \right)}}{\cos^{2}{\left(\frac{\pi}{7} \right)}} + 1}\right) \left(\frac{4 \sin^{4}{\left(\frac{\pi}{28} \right)}}{\sin^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \left(\frac{4 \sin^{4}{\left(\frac{\pi}{14} \right)}}{\sin^{2}{\left(\frac{\pi}{7} \right)}} + 1\right) \sin{\left(\frac{\pi}{14} \right)}}{4 \left(- \frac{4 \sin^{4}{\left(\frac{\pi}{14} \right)}}{\sin^{2}{\left(\frac{\pi}{7} \right)}} + 1\right) \sin^{2}{\left(\frac{\pi}{28} \right)}}$$
/ 2/pi\ \
| cos |--| |
| \7 / |
|-1 + ------------ |
/ 2/pi\ \ / 2/pi\ \ | 4/5*pi\ /pi\ |
| sin |--| | | sin |--| | | 4*sin |----| 4*sin|--| |
2/pi\ | \7 / | | \14/ | | \ 28 / \14/ |
5*sin |--|*|1 + ----------|*|1 + ----------|*|----------------- - -----------------------|
\28/ | 4/pi\| | 4/pi\| | 2/pi\ / 2/pi\\ |
| 4*sin |--|| | 4*sin |--|| | cos |--| | sin |--|| |
\ \14// \ \28// | \7 / | \14/| 2/pi\|
| 1 + ------------ |4 + --------|*sin |--||
| 4/5*pi\ | 4/pi\| \28/|
| 4*sin |----| | sin |--|| |
\ \ 28 / \ \28// /
------------------------------------------------------------------------------------------
/ 2/pi\ \
| sin |--| |
| \7 / | /pi\
|-1 + ----------|*sin|--|
| 4/pi\| \14/
| 4*sin |--||
\ \14//
$$\frac{5 \cdot \left(1 + \frac{\sin^{2}{\left(\frac{\pi}{14} \right)}}{4 \sin^{4}{\left(\frac{\pi}{28} \right)}}\right) \left(1 + \frac{\sin^{2}{\left(\frac{\pi}{7} \right)}}{4 \sin^{4}{\left(\frac{\pi}{14} \right)}}\right) \left(- \frac{4 \sin{\left(\frac{\pi}{14} \right)}}{\left(4 + \frac{\sin^{2}{\left(\frac{\pi}{14} \right)}}{\sin^{4}{\left(\frac{\pi}{28} \right)}}\right) \sin^{2}{\left(\frac{\pi}{28} \right)}} + \frac{-1 + \frac{\cos^{2}{\left(\frac{\pi}{7} \right)}}{4 \sin^{4}{\left(\frac{5 \pi}{28} \right)}}}{1 + \frac{\cos^{2}{\left(\frac{\pi}{7} \right)}}{4 \sin^{4}{\left(\frac{5 \pi}{28} \right)}}}\right) \sin^{2}{\left(\frac{\pi}{28} \right)}}{\left(-1 + \frac{\sin^{2}{\left(\frac{\pi}{7} \right)}}{4 \sin^{4}{\left(\frac{\pi}{14} \right)}}\right) \sin{\left(\frac{\pi}{14} \right)}}$$
/ 2/9*pi\ \
| csc |----| |
| \ 28 / |
|1 - ---------- |
/ 2/3*pi\\ / 2/13*pi\\ | 2/5*pi\ /13*pi\ |
| csc |----|| | csc |-----|| | csc |----| 2*csc|-----| |
| \ 7 /| | \ 28 /| | \ 28 / \ 28 / | /pi\
5*|1 + ----------|*|1 + -----------|*|-------------- - -------------------------|*csc|--|
| 2/pi\ | | 2/pi\ | | 2/9*pi\ / 2/13*pi\\ | \28/
| csc |--| | | csc |--| | | csc |----| | csc |-----|| |
\ \14/ / \ \28/ / | \ 28 / | \ 28 /| /pi\|
|1 + ---------- |1 + -----------|*csc|--||
| 2/5*pi\ | 2/pi\ | \28/|
| csc |----| | csc |--| | |
\ \ 28 / \ \28/ / /
-----------------------------------------------------------------------------------------
/ 2/3*pi\\
| csc |----||
| \ 7 /| /13*pi\
2*|1 - ----------|*csc|-----|
| 2/pi\ | \ 28 /
| csc |--| |
\ \14/ /
$$\frac{5 \left(\frac{\csc^{2}{\left(\frac{13 \pi}{28} \right)}}{\csc^{2}{\left(\frac{\pi}{28} \right)}} + 1\right) \left(\frac{\csc^{2}{\left(\frac{3 \pi}{7} \right)}}{\csc^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \left(- \frac{2 \csc{\left(\frac{13 \pi}{28} \right)}}{\left(\frac{\csc^{2}{\left(\frac{13 \pi}{28} \right)}}{\csc^{2}{\left(\frac{\pi}{28} \right)}} + 1\right) \csc{\left(\frac{\pi}{28} \right)}} + \frac{- \frac{\csc^{2}{\left(\frac{9 \pi}{28} \right)}}{\csc^{2}{\left(\frac{5 \pi}{28} \right)}} + 1}{\frac{\csc^{2}{\left(\frac{9 \pi}{28} \right)}}{\csc^{2}{\left(\frac{5 \pi}{28} \right)}} + 1}\right) \csc{\left(\frac{\pi}{28} \right)}}{2 \left(- \frac{\csc^{2}{\left(\frac{3 \pi}{7} \right)}}{\csc^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \csc{\left(\frac{13 \pi}{28} \right)}}$$
/ 2/5*pi\ \
| sin |----| |
| \ 14 / |
|-1 + ------------ |
/ 2/pi\ \ / 2/pi\ \ | 4/5*pi\ /pi\ |
| sin |--| | | sin |--| | | 4*sin |----| sin|--| |
2/pi\ | \7 / | | \14/ | | \ 28 / \14/ |
5*sin |--|*|1 + ----------|*|1 + ----------|*|----------------- - -------------------------|
\28/ | 4/pi\| | 4/pi\| | 2/5*pi\ / 2/pi\ \ |
| 4*sin |--|| | 4*sin |--|| | sin |----| | sin |--| | |
\ \14// \ \28// | \ 14 / | \14/ | 2/pi\|
| 1 + ------------ |1 + ----------|*sin |--||
| 4/5*pi\ | 4/pi\| \28/|
| 4*sin |----| | 4*sin |--|| |
\ \ 28 / \ \28// /
--------------------------------------------------------------------------------------------
/ 2/pi\ \
| sin |--| |
| \7 / | /pi\
|-1 + ----------|*sin|--|
| 4/pi\| \14/
| 4*sin |--||
\ \14//
$$\frac{5 \cdot \left(1 + \frac{\sin^{2}{\left(\frac{\pi}{14} \right)}}{4 \sin^{4}{\left(\frac{\pi}{28} \right)}}\right) \left(1 + \frac{\sin^{2}{\left(\frac{\pi}{7} \right)}}{4 \sin^{4}{\left(\frac{\pi}{14} \right)}}\right) \left(- \frac{\sin{\left(\frac{\pi}{14} \right)}}{\left(1 + \frac{\sin^{2}{\left(\frac{\pi}{14} \right)}}{4 \sin^{4}{\left(\frac{\pi}{28} \right)}}\right) \sin^{2}{\left(\frac{\pi}{28} \right)}} + \frac{-1 + \frac{\sin^{2}{\left(\frac{5 \pi}{14} \right)}}{4 \sin^{4}{\left(\frac{5 \pi}{28} \right)}}}{1 + \frac{\sin^{2}{\left(\frac{5 \pi}{14} \right)}}{4 \sin^{4}{\left(\frac{5 \pi}{28} \right)}}}\right) \sin^{2}{\left(\frac{\pi}{28} \right)}}{\left(-1 + \frac{\sin^{2}{\left(\frac{\pi}{7} \right)}}{4 \sin^{4}{\left(\frac{\pi}{14} \right)}}\right) \sin{\left(\frac{\pi}{14} \right)}}$$
/ 2/5*pi\ \
| csc |----| |
| \ 28 / |
|-1 + ---------- |
/ 2/pi\ \ / 2/pi\ \ | 2/9*pi\ /pi\ |
| csc |--| | | csc |--| | | csc |----| 2*csc|--| |
| \14/ | | \28/ | | \ 28 / \28/ | /13*pi\
5*|1 + ----------|*|1 + -----------|*|--------------- - ----------------------------|*csc|-----|
| 2/3*pi\| | 2/13*pi\| | 2/5*pi\ / 2/pi\ \ | \ 28 /
| csc |----|| | csc |-----|| | csc |----| | csc |--| | |
\ \ 7 // \ \ 28 // | \ 28 / | \28/ | /13*pi\|
| 1 + ---------- |1 + -----------|*csc|-----||
| 2/9*pi\ | 2/13*pi\| \ 28 /|
| csc |----| | csc |-----|| |
\ \ 28 / \ \ 28 // /
------------------------------------------------------------------------------------------------
/ 2/pi\ \
| csc |--| |
| \14/ | /pi\
2*|-1 + ----------|*csc|--|
| 2/3*pi\| \28/
| csc |----||
\ \ 7 //
$$\frac{5 \cdot \left(1 + \frac{\csc^{2}{\left(\frac{\pi}{28} \right)}}{\csc^{2}{\left(\frac{13 \pi}{28} \right)}}\right) \left(1 + \frac{\csc^{2}{\left(\frac{\pi}{14} \right)}}{\csc^{2}{\left(\frac{3 \pi}{7} \right)}}\right) \left(- \frac{2 \csc{\left(\frac{\pi}{28} \right)}}{\left(1 + \frac{\csc^{2}{\left(\frac{\pi}{28} \right)}}{\csc^{2}{\left(\frac{13 \pi}{28} \right)}}\right) \csc{\left(\frac{13 \pi}{28} \right)}} + \frac{-1 + \frac{\csc^{2}{\left(\frac{5 \pi}{28} \right)}}{\csc^{2}{\left(\frac{9 \pi}{28} \right)}}}{1 + \frac{\csc^{2}{\left(\frac{5 \pi}{28} \right)}}{\csc^{2}{\left(\frac{9 \pi}{28} \right)}}}\right) \csc{\left(\frac{13 \pi}{28} \right)}}{2 \left(-1 + \frac{\csc^{2}{\left(\frac{\pi}{14} \right)}}{\csc^{2}{\left(\frac{3 \pi}{7} \right)}}\right) \csc{\left(\frac{\pi}{28} \right)}}$$
/ 4/5*pi\ \
| 4*sin |----| |
| \ 28 / |
|1 - ------------ |
/ 4/pi\\ / 4/pi\\ | 2/5*pi\ 2/pi\ |
| 4*sin |--|| | 4*sin |--|| | sin |----| 4*sin |--| |
| \14/| | \28/| | \ 14 / \28/ | /pi\
5*|1 + ----------|*|1 + ----------|*|---------------- - ------------------------|*sin|--|
| 2/pi\ | | 2/pi\ | | 4/5*pi\ / 4/pi\\ | \14/
| sin |--| | | sin |--| | | 4*sin |----| | 4*sin |--|| |
\ \7 / / \ \14/ / | \ 28 / | \28/| /pi\|
|1 + ------------ |1 + ----------|*sin|--||
| 2/5*pi\ | 2/pi\ | \14/|
| sin |----| | sin |--| | |
\ \ 14 / \ \14/ / /
-----------------------------------------------------------------------------------------
/ 4/pi\\
| 4*sin |--||
| \14/| 2/pi\
4*|1 - ----------|*sin |--|
| 2/pi\ | \28/
| sin |--| |
\ \7 / /
$$\frac{5 \cdot \left(\frac{4 \sin^{4}{\left(\frac{\pi}{28} \right)}}{\sin^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \left(\frac{4 \sin^{4}{\left(\frac{\pi}{14} \right)}}{\sin^{2}{\left(\frac{\pi}{7} \right)}} + 1\right) \left(- \frac{4 \sin^{2}{\left(\frac{\pi}{28} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{\pi}{28} \right)}}{\sin^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \sin{\left(\frac{\pi}{14} \right)}} + \frac{- \frac{4 \sin^{4}{\left(\frac{5 \pi}{28} \right)}}{\sin^{2}{\left(\frac{5 \pi}{14} \right)}} + 1}{\frac{4 \sin^{4}{\left(\frac{5 \pi}{28} \right)}}{\sin^{2}{\left(\frac{5 \pi}{14} \right)}} + 1}\right) \sin{\left(\frac{\pi}{14} \right)}}{4 \left(- \frac{4 \sin^{4}{\left(\frac{\pi}{14} \right)}}{\sin^{2}{\left(\frac{\pi}{7} \right)}} + 1\right) \sin^{2}{\left(\frac{\pi}{28} \right)}}$$
/ 2/5*pi\ \
| sec |----| |
| \ 28 / |
|1 - ----------- |
/ 2/pi\ \ / 2/pi\ \ | 2/-9*pi\ /pi\ |
| sec |--| | | sec |--| | | sec |-----| 2*sec|--| |
| \28/ | | \14/ | | \ 28 / \28/ | /-13*pi\
5*|1 + ------------|*|1 + -----------|*|--------------- - ------------------------------|*sec|------|
| 2/-13*pi\| | 2/-3*pi\| | 2/5*pi\ / 2/pi\ \ | \ 28 /
| sec |------|| | sec |-----|| | sec |----| | sec |--| | |
\ \ 28 // \ \ 7 // | \ 28 / | \28/ | /-13*pi\|
|1 + ----------- |1 + ------------|*sec|------||
| 2/-9*pi\ | 2/-13*pi\| \ 28 /|
| sec |-----| | sec |------|| |
\ \ 28 / \ \ 28 // /
-----------------------------------------------------------------------------------------------------
/ 2/pi\ \
| sec |--| |
| \14/ | /pi\
2*|1 - -----------|*sec|--|
| 2/-3*pi\| \28/
| sec |-----||
\ \ 7 //
$$\frac{5 \left(\frac{\sec^{2}{\left(\frac{\pi}{28} \right)}}{\sec^{2}{\left(- \frac{13 \pi}{28} \right)}} + 1\right) \left(\frac{\sec^{2}{\left(\frac{\pi}{14} \right)}}{\sec^{2}{\left(- \frac{3 \pi}{7} \right)}} + 1\right) \left(- \frac{2 \sec{\left(\frac{\pi}{28} \right)}}{\left(\frac{\sec^{2}{\left(\frac{\pi}{28} \right)}}{\sec^{2}{\left(- \frac{13 \pi}{28} \right)}} + 1\right) \sec{\left(- \frac{13 \pi}{28} \right)}} + \frac{- \frac{\sec^{2}{\left(\frac{5 \pi}{28} \right)}}{\sec^{2}{\left(- \frac{9 \pi}{28} \right)}} + 1}{\frac{\sec^{2}{\left(\frac{5 \pi}{28} \right)}}{\sec^{2}{\left(- \frac{9 \pi}{28} \right)}} + 1}\right) \sec{\left(- \frac{13 \pi}{28} \right)}}{2 \left(- \frac{\sec^{2}{\left(\frac{\pi}{14} \right)}}{\sec^{2}{\left(- \frac{3 \pi}{7} \right)}} + 1\right) \sec{\left(\frac{\pi}{28} \right)}}$$
/ 2/-9*pi\ \
| cos |-----| |
| \ 28 / |
|1 - ----------- |
/ 2/-13*pi\\ / 2/-3*pi\\ | 2/5*pi\ /-13*pi\ |
| cos |------|| | cos |-----|| | cos |----| 2*cos|------| |
| \ 28 /| | \ 7 /| | \ 28 / \ 28 / | /pi\
5*|1 + ------------|*|1 + -----------|*|--------------- - --------------------------|*cos|--|
| 2/pi\ | | 2/pi\ | | 2/-9*pi\ / 2/-13*pi\\ | \28/
| cos |--| | | cos |--| | | cos |-----| | cos |------|| |
\ \28/ / \ \14/ / | \ 28 / | \ 28 /| /pi\|
|1 + ----------- |1 + ------------|*cos|--||
| 2/5*pi\ | 2/pi\ | \28/|
| cos |----| | cos |--| | |
\ \ 28 / \ \28/ / /
---------------------------------------------------------------------------------------------
/ 2/-3*pi\\
| cos |-----||
| \ 7 /| /-13*pi\
2*|1 - -----------|*cos|------|
| 2/pi\ | \ 28 /
| cos |--| |
\ \14/ /
$$\frac{5 \left(\frac{\cos^{2}{\left(- \frac{13 \pi}{28} \right)}}{\cos^{2}{\left(\frac{\pi}{28} \right)}} + 1\right) \left(\frac{\cos^{2}{\left(- \frac{3 \pi}{7} \right)}}{\cos^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \left(- \frac{2 \cos{\left(- \frac{13 \pi}{28} \right)}}{\left(\frac{\cos^{2}{\left(- \frac{13 \pi}{28} \right)}}{\cos^{2}{\left(\frac{\pi}{28} \right)}} + 1\right) \cos{\left(\frac{\pi}{28} \right)}} + \frac{- \frac{\cos^{2}{\left(- \frac{9 \pi}{28} \right)}}{\cos^{2}{\left(\frac{5 \pi}{28} \right)}} + 1}{\frac{\cos^{2}{\left(- \frac{9 \pi}{28} \right)}}{\cos^{2}{\left(\frac{5 \pi}{28} \right)}} + 1}\right) \cos{\left(\frac{\pi}{28} \right)}}{2 \left(- \frac{\cos^{2}{\left(- \frac{3 \pi}{7} \right)}}{\cos^{2}{\left(\frac{\pi}{14} \right)}} + 1\right) \cos{\left(- \frac{13 \pi}{28} \right)}}$$
/ 2/5*pi\ \
| cos |----| |
| \ 28 / |
|-1 + ----------- |
/ 2/pi\ \ / 2/pi\ \ | 2/-9*pi\ /pi\ |
| cos |--| | | cos |--| | | cos |-----| 2*cos|--| |
| \28/ | | \14/ | | \ 28 / \28/ | /-13*pi\
5*|1 + ------------|*|1 + -----------|*|---------------- - ------------------------------|*cos|------|
| 2/-13*pi\| | 2/-3*pi\| | 2/5*pi\ / 2/pi\ \ | \ 28 /
| cos |------|| | cos |-----|| | cos |----| | cos |--| | |
\ \ 28 // \ \ 7 // | \ 28 / | \28/ | /-13*pi\|
|1 + ----------- |1 + ------------|*cos|------||
| 2/-9*pi\ | 2/-13*pi\| \ 28 /|
| cos |-----| | cos |------|| |
\ \ 28 / \ \ 28 // /
------------------------------------------------------------------------------------------------------
/ 2/pi\ \
| cos |--| |
| \14/ | /pi\
2*|-1 + -----------|*cos|--|
| 2/-3*pi\| \28/
| cos |-----||
\ \ 7 //
$$\frac{5 \cdot \left(1 + \frac{\cos^{2}{\left(\frac{\pi}{28} \right)}}{\cos^{2}{\left(- \frac{13 \pi}{28} \right)}}\right) \left(1 + \frac{\cos^{2}{\left(\frac{\pi}{14} \right)}}{\cos^{2}{\left(- \frac{3 \pi}{7} \right)}}\right) \left(- \frac{2 \cos{\left(\frac{\pi}{28} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{\pi}{28} \right)}}{\cos^{2}{\left(- \frac{13 \pi}{28} \right)}}\right) \cos{\left(- \frac{13 \pi}{28} \right)}} + \frac{-1 + \frac{\cos^{2}{\left(\frac{5 \pi}{28} \right)}}{\cos^{2}{\left(- \frac{9 \pi}{28} \right)}}}{1 + \frac{\cos^{2}{\left(\frac{5 \pi}{28} \right)}}{\cos^{2}{\left(- \frac{9 \pi}{28} \right)}}}\right) \cos{\left(- \frac{13 \pi}{28} \right)}}{2 \left(-1 + \frac{\cos^{2}{\left(\frac{\pi}{14} \right)}}{\cos^{2}{\left(- \frac{3 \pi}{7} \right)}}\right) \cos{\left(\frac{\pi}{28} \right)}}$$
/ 2/-9*pi\ \
| sec |-----| |
| \ 28 / |
|-1 + ----------- |
/ 2/-13*pi\\ / 2/-3*pi\\ | 2/5*pi\ /-13*pi\ |
| sec |------|| | sec |-----|| | sec |----| 2*sec|------| |
| \ 28 /| | \ 7 /| | \ 28 / \ 28 / | /pi\
5*|1 + ------------|*|1 + -----------|*|---------------- - --------------------------|*sec|--|
| 2/pi\ | | 2/pi\ | | 2/-9*pi\ / 2/-13*pi\\ | \28/
| sec |--| | | sec |--| | | sec |-----| | sec |------|| |
\ \28/ / \ \14/ / | \ 28 / | \ 28 /| /pi\|
|1 + ----------- |1 + ------------|*sec|--||
| 2/5*pi\ | 2/pi\ | \28/|
| sec |----| | sec |--| | |
\ \ 28 / \ \28/ / /
----------------------------------------------------------------------------------------------
/ 2/-3*pi\\
| sec |-----||
| \ 7 /| /-13*pi\
2*|-1 + -----------|*sec|------|
| 2/pi\ | \ 28 /
| sec |--| |
\ \14/ /
$$\frac{5 \cdot \left(1 + \frac{\sec^{2}{\left(- \frac{13 \pi}{28} \right)}}{\sec^{2}{\left(\frac{\pi}{28} \right)}}\right) \left(1 + \frac{\sec^{2}{\left(- \frac{3 \pi}{7} \right)}}{\sec^{2}{\left(\frac{\pi}{14} \right)}}\right) \left(- \frac{2 \sec{\left(- \frac{13 \pi}{28} \right)}}{\left(1 + \frac{\sec^{2}{\left(- \frac{13 \pi}{28} \right)}}{\sec^{2}{\left(\frac{\pi}{28} \right)}}\right) \sec{\left(\frac{\pi}{28} \right)}} + \frac{-1 + \frac{\sec^{2}{\left(- \frac{9 \pi}{28} \right)}}{\sec^{2}{\left(\frac{5 \pi}{28} \right)}}}{1 + \frac{\sec^{2}{\left(- \frac{9 \pi}{28} \right)}}{\sec^{2}{\left(\frac{5 \pi}{28} \right)}}}\right) \sec{\left(\frac{\pi}{28} \right)}}{2 \left(-1 + \frac{\sec^{2}{\left(- \frac{3 \pi}{7} \right)}}{\sec^{2}{\left(\frac{\pi}{14} \right)}}\right) \sec{\left(- \frac{13 \pi}{28} \right)}}$$
5*(1 + sec(-13*pi/28)^2/sec(pi/28)^2)*(1 + sec(-3*pi/7)^2/sec(pi/14)^2)*((-1 + sec(-9*pi/28)^2/sec(5*pi/28)^2)/(1 + sec(-9*pi/28)^2/sec(5*pi/28)^2) - 2*sec(-13*pi/28)/((1 + sec(-13*pi/28)^2/sec(pi/28)^2)*sec(pi/28)))*sec(pi/28)/(2*(-1 + sec(-3*pi/7)^2/sec(pi/14)^2)*sec(-13*pi/28))