Господин Экзамен
Общий знаменатель (sin(-29*pi/6)*cos(-19*pi/3))/(sin(56)^(2)+1+sin(124)^(2))
Решение
Вы ввели
[src]
/-29*pi\ /-19*pi\ sin|------|*cos|------| \ 6 / \ 3 / ------------------------ 2 2 sin (56) + 1 + sin (124)
$$\frac{\sin{\left(- \frac{29 \pi}{6} \right)} \cos{\left(- \frac{19 \pi}{3} \right)}}{\sin^{2}{\left(56 \right)} + \sin^{2}{\left(124 \right)} + 1}$$
sin(-29*pi/6)*cos(-19*pi/3)/(sin(56)^2 + 1 + sin(124)^2)
Общее упрощение
[src]
-1
----------------------------
2 2
4 + 4*sin (56) + 4*sin (124)
$$- \frac{1}{4 \sin^{2}{\left(56 \right)} + 4 \sin^{2}{\left(124 \right)} + 4}$$
-1/(4 + 4*sin(56)^2 + 4*sin(124)^2)
Собрать выражение
[src]
1 ---------------------------- 2*(-4 + cos(112) + cos(248))
$$\frac{1}{2 \left(-4 + \cos{\left(248 \right)} + \cos{\left(112 \right)}\right)}$$
1/(2*(-4 + cos(112) + cos(248)))
Степени
[src]
-1 ---------------------------- / 2 2 \ 4*\sin (56) + 1 + sin (124)/
$$- \frac{1}{4 \left(\sin^{2}{\left(56 \right)} + \sin^{2}{\left(124 \right)} + 1\right)}$$
-1 ---------------------------- / 2 2 \ 4*\1 + sin (56) + sin (124)/
$$- \frac{1}{4 \left(\sin^{2}{\left(56 \right)} + \sin^{2}{\left(124 \right)} + 1\right)}$$
/ -pi*I pi*I\
| ------ ----| / 5*pi*I -5*pi*I\
| 3 3 | | ------ -------|
|e e | | 6 6 |
-I*|------- + -----|*\- e + e /
\ 2 2 /
---------------------------------------------------
/ 2 2\
| / -124*I 124*I\ / -56*I 56*I\ |
| \- e + e / \- e + e / |
2*|1 - --------------------- - -------------------|
\ 4 4 /
$$- \frac{i \left(e^{- \frac{5 i \pi}{6}} - e^{\frac{5 i \pi}{6}}\right) \left(\frac{e^{- \frac{i \pi}{3}}}{2} + \frac{e^{\frac{i \pi}{3}}}{2}\right)}{2 \cdot \left(1 - \frac{\left(e^{124 i} - e^{- 124 i}\right)^{2}}{4} - \frac{\left(- e^{- 56 i} + e^{56 i}\right)^{2}}{4}\right)}$$
-i*(exp(-pi*i/3)/2 + exp(pi*i/3)/2)*(-exp(5*pi*i/6) + exp(-5*pi*i/6))/(2*(1 - (-exp(-124*i) + exp(124*i))^2/4 - (-exp(-56*i) + exp(56*i))^2/4))
Объединение рациональных выражений
[src]
-1 ---------------------------- / 2 2 \ 4*\1 + sin (56) + sin (124)/
$$- \frac{1}{4 \left(\sin^{2}{\left(56 \right)} + \sin^{2}{\left(124 \right)} + 1\right)}$$
-1/(4*(1 + sin(56)^2 + sin(124)^2))
Рациональный знаменатель
[src]
-1
----------------------------
2 2
4 + 4*sin (56) + 4*sin (124)
$$- \frac{1}{4 \sin^{2}{\left(56 \right)} + 4 \sin^{2}{\left(124 \right)} + 4}$$
-1/(4 + 4*sin(56)^2 + 4*sin(124)^2)
Комбинаторика
[src]
-1 ---------------------------- / 2 2 \ 4*\1 + sin (56) + sin (124)/
$$- \frac{1}{4 \left(\sin^{2}{\left(56 \right)} + \sin^{2}{\left(124 \right)} + 1\right)}$$
-1/(4*(1 + sin(56)^2 + sin(124)^2))
Общий знаменатель
[src]
-1
----------------------------
2 2
4 + 4*sin (56) + 4*sin (124)
$$- \frac{1}{4 \sin^{2}{\left(56 \right)} + 4 \sin^{2}{\left(124 \right)} + 4}$$
-1/(4 + 4*sin(56)^2 + 4*sin(124)^2)
Тригонометрическая часть
[src]
-1
----------------------------
2 2
4 + 4*sin (56) + 4*sin (124)
$$- \frac{1}{4 \sin^{2}{\left(56 \right)} + 4 \sin^{2}{\left(124 \right)} + 4}$$
1 ---------------------------- 2*(-4 + cos(112) + cos(248))
$$\frac{1}{2 \left(-4 + \cos{\left(248 \right)} + \cos{\left(112 \right)}\right)}$$
-1 ---------------------------- / 2 2 \ 4*\sin (56) + 1 + sin (124)/
$$- \frac{1}{4 \left(\sin^{2}{\left(56 \right)} + \sin^{2}{\left(124 \right)} + 1\right)}$$
-1 ---------------------------- / 2 2 \ 4*\1 + sin (56) + sin (124)/
$$- \frac{1}{4 \left(\sin^{2}{\left(56 \right)} + \sin^{2}{\left(124 \right)} + 1\right)}$$
-1 ---------------------------- / 1 1 \ 4*|1 + -------- + ---------| | 2 2 | \ csc (56) csc (124)/
$$- \frac{1}{4 \left(\frac{1}{\csc^{2}{\left(56 \right)}} + \frac{1}{\csc^{2}{\left(124 \right)}} + 1\right)}$$
/-29*pi\
sin|------|
\ 6 /
----------------------------
/ 2 2 \
2*\1 + sin (56) + sin (124)/
$$\frac{\sin{\left(- \frac{29 \pi}{6} \right)}}{2 \left(\sin^{2}{\left(56 \right)} + \sin^{2}{\left(124 \right)} + 1\right)}$$
-1 -------------------------------------- / 2/ pi\ 2/ pi\\ 4*|1 + cos |56 - --| + cos |124 - --|| \ \ 2 / \ 2 //
$$- \frac{1}{4 \left(\cos^{2}{\left(- \frac{\pi}{2} + 56 \right)} + \cos^{2}{\left(- \frac{\pi}{2} + 124 \right)} + 1\right)}$$
/-35*pi\
-sin|------|
\ 6 /
----------------------------
/ 2 2 \
2*\1 + sin (56) + sin (124)/
$$- \frac{\sin{\left(- \frac{35 \pi}{6} \right)}}{2 \left(\sin^{2}{\left(56 \right)} + \sin^{2}{\left(124 \right)} + 1\right)}$$
___
4 + 2*\/ 3
---------------------------------------------
/ 2\
| / ___\ |
\1 + \2 + \/ 3 / /*(-4 + cos(112) + cos(248))
$$\frac{2 \sqrt{3} + 4}{\left(1 + \left(\sqrt{3} + 2\right)^{2}\right) \left(-4 + \cos{\left(248 \right)} + \cos{\left(112 \right)}\right)}$$
-1 ---------------------------------------- / 1 1 \ 4*|1 + --------------- + --------------| | 2/ pi\ 2/ pi\| | sec |-124 + --| sec |-56 + --|| \ \ 2 / \ 2 //
$$- \frac{1}{4 \left(\frac{1}{\sec^{2}{\left(-56 + \frac{\pi}{2} \right)}} + \frac{1}{\sec^{2}{\left(-124 + \frac{\pi}{2} \right)}} + 1\right)}$$
/ ___\
-\-4 - 2*\/ 3 /
----------------------------------------------
/ 2\
| / ___\ |
\1 + \-2 - \/ 3 / /*(-4 + cos(112) + cos(248))
$$- \frac{-4 - 2 \sqrt{3}}{\left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(-4 + \cos{\left(248 \right)} + \cos{\left(112 \right)}\right)}$$
/ ___\
-\-4 + 2*\/ 3 /
----------------------------------------------
/ 2\
| / ___\ |
\1 + \-2 + \/ 3 / /*(-4 + cos(112) + cos(248))
$$- \frac{-4 + 2 \sqrt{3}}{\left(\left(-2 + \sqrt{3}\right)^{2} + 1\right) \left(-4 + \cos{\left(248 \right)} + \cos{\left(112 \right)}\right)}$$
___
4 - 2*\/ 3
---------------------------------------------
/ 2\
| / ___\ |
\1 + \2 - \/ 3 / /*(-4 + cos(112) + cos(248))
$$\frac{- 2 \sqrt{3} + 4}{\left(\left(- \sqrt{3} + 2\right)^{2} + 1\right) \left(-4 + \cos{\left(248 \right)} + \cos{\left(112 \right)}\right)}$$
-1 -------------------------------------- / 1 1 \ 4*|1 + ------------- + --------------| | 2/ pi\ 2/ pi\| | sec |56 - --| sec |124 - --|| \ \ 2 / \ 2 //
$$- \frac{1}{4 \left(\frac{1}{\sec^{2}{\left(- \frac{\pi}{2} + 56 \right)}} + \frac{1}{\sec^{2}{\left(- \frac{\pi}{2} + 124 \right)}} + 1\right)}$$
1 --------------------------------------------------- / 1 1 \ /35*pi\ 2*|1 + --------------- + --------------|*csc|-----| | 2 2 | \ 6 / \ csc (-124 + pi) csc (-56 + pi)/
$$\frac{1}{2 \left(\frac{1}{\csc^{2}{\left(-56 + \pi \right)}} + \frac{1}{\csc^{2}{\left(-124 + \pi \right)}} + 1\right) \csc{\left(\frac{35 \pi}{6} \right)}}$$
/-16*pi\
cos|------|
\ 3 /
--------------------------------------
/ 2/ pi\ 2/ pi\\
2*|1 + cos |56 - --| + cos |124 - --||
\ \ 2 / \ 2 //
$$\frac{\cos{\left(- \frac{16 \pi}{3} \right)}}{2 \left(\cos^{2}{\left(- \frac{\pi}{2} + 56 \right)} + \cos^{2}{\left(- \frac{\pi}{2} + 124 \right)} + 1\right)}$$
/-19*pi\
-cos|------|
\ 3 /
--------------------------------------
/ 2/ pi\ 2/ pi\\
2*|1 + cos |56 - --| + cos |124 - --||
\ \ 2 / \ 2 //
$$- \frac{\cos{\left(- \frac{19 \pi}{3} \right)}}{2 \left(\cos^{2}{\left(- \frac{\pi}{2} + 56 \right)} + \cos^{2}{\left(- \frac{\pi}{2} + 124 \right)} + 1\right)}$$
/ ___\
-\-4 - 2*\/ 3 /
----------------------------------------------
/ 2\
| / ___\ | / 1 1 \
\1 + \-2 - \/ 3 / /*|-4 + -------- + --------|
\ sec(112) sec(248)/
$$- \frac{-4 - 2 \sqrt{3}}{\left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(-4 + \frac{1}{\sec{\left(248 \right)}} + \frac{1}{\sec{\left(112 \right)}}\right)}$$
/-19*pi\ /-29*pi\
cos|------|*sin|------|
\ 3 / \ 6 /
-----------------------
cos(112) cos(248)
2 - -------- - --------
2 2
$$\frac{\sin{\left(- \frac{29 \pi}{6} \right)} \cos{\left(- \frac{19 \pi}{3} \right)}}{- \frac{\cos{\left(112 \right)}}{2} - \frac{\cos{\left(248 \right)}}{2} + 2}$$
/ ___\
-\-4 + 2*\/ 3 /
----------------------------------------------
/ 2\
| / ___\ | / 1 1 \
\1 + \-2 + \/ 3 / /*|-4 + -------- + --------|
\ sec(112) sec(248)/
$$- \frac{-4 + 2 \sqrt{3}}{\left(\left(-2 + \sqrt{3}\right)^{2} + 1\right) \left(-4 + \frac{1}{\sec{\left(248 \right)}} + \frac{1}{\sec{\left(112 \right)}}\right)}$$
/ ___\
-\-4 + 2*\/ 3 /
--------------------------------------------------------
/ 2\
| / ___\ | / / pi\ / pi\\
\1 + \-2 + \/ 3 / /*|-4 + sin|112 + --| + sin|248 + --||
\ \ 2 / \ 2 //
$$- \frac{-4 + 2 \sqrt{3}}{\left(\left(-2 + \sqrt{3}\right)^{2} + 1\right) \left(-4 + \sin{\left(\frac{\pi}{2} + 248 \right)} + \sin{\left(\frac{\pi}{2} + 112 \right)}\right)}$$
/ ___\
-\-4 - 2*\/ 3 /
--------------------------------------------------------
/ 2\
| / ___\ | / / pi\ / pi\\
\1 + \-2 - \/ 3 / /*|-4 + sin|112 + --| + sin|248 + --||
\ \ 2 / \ 2 //
$$- \frac{-4 - 2 \sqrt{3}}{\left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(-4 + \sin{\left(\frac{\pi}{2} + 248 \right)} + \sin{\left(\frac{\pi}{2} + 112 \right)}\right)}$$
1 -------------------------------------------------- / 1 1 \ /-16*pi\ 2*|1 + ------------- + --------------|*sec|------| | 2/ pi\ 2/ pi\| \ 3 / | sec |56 - --| sec |124 - --|| \ \ 2 / \ 2 //
$$\frac{1}{2 \left(\frac{1}{\sec^{2}{\left(- \frac{\pi}{2} + 56 \right)}} + \frac{1}{\sec^{2}{\left(- \frac{\pi}{2} + 124 \right)}} + 1\right) \sec{\left(- \frac{16 \pi}{3} \right)}}$$
-1 -------------------------------------------------- / 1 1 \ /-19*pi\ 2*|1 + ------------- + --------------|*sec|------| | 2/ pi\ 2/ pi\| \ 3 / | sec |56 - --| sec |124 - --|| \ \ 2 / \ 2 //
$$- \frac{1}{2 \left(\frac{1}{\sec^{2}{\left(- \frac{\pi}{2} + 56 \right)}} + \frac{1}{\sec^{2}{\left(- \frac{\pi}{2} + 124 \right)}} + 1\right) \sec{\left(- \frac{19 \pi}{3} \right)}}$$
/ ___\
-\-4 + 2*\/ 3 /
---------------------------------------------------
/ 2\ / 2 \
| / ___\ | | 1 - tan (124) |
\1 + \-2 + \/ 3 / /*|-4 + ------------- + cos(112)|
| 2 |
\ 1 + tan (124) /
$$- \frac{-4 + 2 \sqrt{3}}{\left(\left(-2 + \sqrt{3}\right)^{2} + 1\right) \left(-4 + \frac{- \tan^{2}{\left(124 \right)} + 1}{1 + \tan^{2}{\left(124 \right)}} + \cos{\left(112 \right)}\right)}$$
/ ___\
-\-4 - 2*\/ 3 /
---------------------------------------------------
/ 2\ / 2 \
| / ___\ | | 1 - tan (124) |
\1 + \-2 - \/ 3 / /*|-4 + ------------- + cos(112)|
| 2 |
\ 1 + tan (124) /
$$- \frac{-4 - 2 \sqrt{3}}{\left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(-4 + \frac{- \tan^{2}{\left(124 \right)} + 1}{1 + \tan^{2}{\left(124 \right)}} + \cos{\left(112 \right)}\right)}$$
/ ___\
-\-4 + 2*\/ 3 /
----------------------------------------------------------
/ 2\
| / ___\ | / 1 1 \
\1 + \-2 + \/ 3 / /*|-4 + -------------- + --------------|
| / pi\ / pi\|
| csc|-248 + --| csc|-112 + --||
\ \ 2 / \ 2 //
$$- \frac{-4 + 2 \sqrt{3}}{\left(\left(-2 + \sqrt{3}\right)^{2} + 1\right) \left(-4 + \frac{1}{\csc{\left(-248 + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(-112 + \frac{\pi}{2} \right)}}\right)}$$
/ ___\
-\-4 - 2*\/ 3 /
----------------------------------------------------------
/ 2\
| / ___\ | / 1 1 \
\1 + \-2 - \/ 3 / /*|-4 + -------------- + --------------|
| / pi\ / pi\|
| csc|-248 + --| csc|-112 + --||
\ \ 2 / \ 2 //
$$- \frac{-4 - 2 \sqrt{3}}{\left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(-4 + \frac{1}{\csc{\left(-248 + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(-112 + \frac{\pi}{2} \right)}}\right)}$$
-1 ----------------------------------------- / 2 2 \ | 4*cot (28) 4*cot (62) | 4*|1 + --------------- + ---------------| | 2 2| | / 2 \ / 2 \ | \ \1 + cot (28)/ \1 + cot (62)/ /
$$- \frac{1}{4 \cdot \left(\frac{4 \cot^{2}{\left(28 \right)}}{\left(1 + \cot^{2}{\left(28 \right)}\right)^{2}} + \frac{4 \cot^{2}{\left(62 \right)}}{\left(\cot^{2}{\left(62 \right)} + 1\right)^{2}} + 1\right)}$$
-1 ----------------------------------------- / 2 2 \ | 4*tan (28) 4*tan (62) | 4*|1 + --------------- + ---------------| | 2 2| | / 2 \ / 2 \ | \ \1 + tan (28)/ \1 + tan (62)/ /
$$- \frac{1}{4 \cdot \left(\frac{4 \tan^{2}{\left(28 \right)}}{\left(\tan^{2}{\left(28 \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(62 \right)}}{\left(1 + \tan^{2}{\left(62 \right)}\right)^{2}} + 1\right)}$$
/ ___\
-\-4 + 2*\/ 3 /
---------------------------------------------------------
/ 2\ / 2 2 \
| / ___\ | | -1 + cot (56) -1 + cot (124)|
\1 + \-2 + \/ 3 / /*|-4 + ------------- + --------------|
| 2 2 |
\ 1 + cot (56) 1 + cot (124) /
$$- \frac{-4 + 2 \sqrt{3}}{\left(\left(-2 + \sqrt{3}\right)^{2} + 1\right) \left(-4 + \frac{-1 + \cot^{2}{\left(124 \right)}}{\cot^{2}{\left(124 \right)} + 1} + \frac{-1 + \cot^{2}{\left(56 \right)}}{1 + \cot^{2}{\left(56 \right)}}\right)}$$
/ ___\
-\-4 - 2*\/ 3 /
---------------------------------------------------------
/ 2\ / 2 2 \
| / ___\ | | -1 + cot (56) -1 + cot (124)|
\1 + \-2 - \/ 3 / /*|-4 + ------------- + --------------|
| 2 2 |
\ 1 + cot (56) 1 + cot (124) /
$$- \frac{-4 - 2 \sqrt{3}}{\left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(-4 + \frac{-1 + \cot^{2}{\left(124 \right)}}{\cot^{2}{\left(124 \right)} + 1} + \frac{-1 + \cot^{2}{\left(56 \right)}}{1 + \cot^{2}{\left(56 \right)}}\right)}$$
/ ___\
-\-4 - 2*\/ 3 /
-------------------------------------------------------
/ 2\ / 2 2 \
| / ___\ | | 1 - tan (56) 1 - tan (124)|
\1 + \-2 - \/ 3 / /*|-4 + ------------ + -------------|
| 2 2 |
\ 1 + tan (56) 1 + tan (124)/
$$- \frac{-4 - 2 \sqrt{3}}{\left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(-4 + \frac{- \tan^{2}{\left(124 \right)} + 1}{1 + \tan^{2}{\left(124 \right)}} + \frac{- \tan^{2}{\left(56 \right)} + 1}{\tan^{2}{\left(56 \right)} + 1}\right)}$$
/ ___\
-\-4 + 2*\/ 3 /
-------------------------------------------------------
/ 2\ / 2 2 \
| / ___\ | | 1 - tan (56) 1 - tan (124)|
\1 + \-2 + \/ 3 / /*|-4 + ------------ + -------------|
| 2 2 |
\ 1 + tan (56) 1 + tan (124)/
$$- \frac{-4 + 2 \sqrt{3}}{\left(\left(-2 + \sqrt{3}\right)^{2} + 1\right) \left(-4 + \frac{- \tan^{2}{\left(124 \right)} + 1}{1 + \tan^{2}{\left(124 \right)}} + \frac{- \tan^{2}{\left(56 \right)} + 1}{\tan^{2}{\left(56 \right)} + 1}\right)}$$
___
-4 + 2*\/ 3
-------------------------------------------------------------
/ 2\ / 2 2 \
| / ___\ | | 4*cot (28) 4*cot (62) |
2*\1 + \-2 + \/ 3 / /*|1 + --------------- + ---------------|
| 2 2|
| / 2 \ / 2 \ |
\ \1 + cot (28)/ \1 + cot (62)/ /
$$\frac{-4 + 2 \sqrt{3}}{2 \left(\left(-2 + \sqrt{3}\right)^{2} + 1\right) \left(\frac{4 \cot^{2}{\left(28 \right)}}{\left(1 + \cot^{2}{\left(28 \right)}\right)^{2}} + \frac{4 \cot^{2}{\left(62 \right)}}{\left(\cot^{2}{\left(62 \right)} + 1\right)^{2}} + 1\right)}$$
/ ___\
-\4 - 2*\/ 3 /
------------------------------------------------------------
/ 2\ / 2 2 \
| / ___\ | | 4*tan (28) 4*tan (62) |
2*\1 + \2 - \/ 3 / /*|1 + --------------- + ---------------|
| 2 2|
| / 2 \ / 2 \ |
\ \1 + tan (28)/ \1 + tan (62)/ /
$$- \frac{- 2 \sqrt{3} + 4}{2 \left(\left(- \sqrt{3} + 2\right)^{2} + 1\right) \left(\frac{4 \tan^{2}{\left(28 \right)}}{\left(\tan^{2}{\left(28 \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(62 \right)}}{\left(1 + \tan^{2}{\left(62 \right)}\right)^{2}} + 1\right)}$$
___
-4 - 2*\/ 3
-------------------------------------------------------------
/ 2\ / 2 2 \
| / ___\ | | 4*tan (28) 4*tan (62) |
2*\1 + \-2 - \/ 3 / /*|1 + --------------- + ---------------|
| 2 2|
| / 2 \ / 2 \ |
\ \1 + tan (28)/ \1 + tan (62)/ /
$$\frac{-4 - 2 \sqrt{3}}{2 \cdot \left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(\frac{4 \tan^{2}{\left(28 \right)}}{\left(\tan^{2}{\left(28 \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(62 \right)}}{\left(1 + \tan^{2}{\left(62 \right)}\right)^{2}} + 1\right)}$$
/ ___\
-\4 + 2*\/ 3 /
------------------------------------------------------------
/ 2\ / 2 2 \
| / ___\ | | 4*cot (28) 4*cot (62) |
2*\1 + \2 + \/ 3 / /*|1 + --------------- + ---------------|
| 2 2|
| / 2 \ / 2 \ |
\ \1 + cot (28)/ \1 + cot (62)/ /
$$- \frac{2 \sqrt{3} + 4}{2 \cdot \left(1 + \left(\sqrt{3} + 2\right)^{2}\right) \left(\frac{4 \cot^{2}{\left(28 \right)}}{\left(1 + \cot^{2}{\left(28 \right)}\right)^{2}} + \frac{4 \cot^{2}{\left(62 \right)}}{\left(\cot^{2}{\left(62 \right)} + 1\right)^{2}} + 1\right)}$$
___
-4 + 2*\/ 3
-------------------------------------------------------------------------------
/ 2\
| / ___\ | / 4 4 \
2*\1 + \-2 + \/ 3 / /*|1 + ------------------------ + ------------------------|
| 2 2 |
| / 1 \ 2 / 1 \ 2 |
| |1 + --------| *tan (28) |1 + --------| *tan (62)|
| | 2 | | 2 | |
\ \ tan (28)/ \ tan (62)/ /
$$\frac{-4 + 2 \sqrt{3}}{2 \left(\left(-2 + \sqrt{3}\right)^{2} + 1\right) \left(\frac{4}{\left(1 + \frac{1}{\tan^{2}{\left(28 \right)}}\right)^{2} \tan^{2}{\left(28 \right)}} + \frac{4}{\left(\frac{1}{\tan^{2}{\left(62 \right)}} + 1\right)^{2} \tan^{2}{\left(62 \right)}} + 1\right)}$$
___
-4 - 2*\/ 3
-------------------------------------------------------------------------------
/ 2\
| / ___\ | / 4 4 \
2*\1 + \-2 - \/ 3 / /*|1 + ------------------------ + ------------------------|
| 2 2 |
| / 1 \ 2 / 1 \ 2 |
| |1 + --------| *cot (28) |1 + --------| *cot (62)|
| | 2 | | 2 | |
\ \ cot (28)/ \ cot (62)/ /
$$\frac{-4 - 2 \sqrt{3}}{2 \cdot \left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(\frac{4}{\left(\frac{1}{\cot^{2}{\left(28 \right)}} + 1\right)^{2} \cot^{2}{\left(28 \right)}} + \frac{4}{\left(1 + \frac{1}{\cot^{2}{\left(62 \right)}}\right)^{2} \cot^{2}{\left(62 \right)}} + 1\right)}$$
-1 ----------------------------------------------------- / 2 2\ | / 2/ pi\\ / 2/ pi\\ | | |-1 + tan |28 + --|| |-1 + tan |62 + --|| | | \ \ 4 // \ \ 4 // | 4*|1 + --------------------- + ---------------------| | 2 2| | / 2/ pi\\ / 2/ pi\\ | | |1 + tan |28 + --|| |1 + tan |62 + --|| | \ \ \ 4 // \ \ 4 // /
$$- \frac{1}{4 \left(\frac{\left(-1 + \tan^{2}{\left(\frac{\pi}{4} + 28 \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{\pi}{4} + 28 \right)} + 1\right)^{2}} + \frac{\left(-1 + \tan^{2}{\left(\frac{\pi}{4} + 62 \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{\pi}{4} + 62 \right)} + 1\right)^{2}} + 1\right)}$$
-1 --------------------------------------------------- / 2 2\ | / 2/ pi\\ / 2/ pi\\ | | |1 - cot |28 + --|| |1 - cot |62 + --|| | | \ \ 4 // \ \ 4 // | 4*|1 + -------------------- + --------------------| | 2 2| | / 2/ pi\\ / 2/ pi\\ | | |1 + cot |28 + --|| |1 + cot |62 + --|| | \ \ \ 4 // \ \ 4 // /
$$- \frac{1}{4 \left(\frac{\left(- \cot^{2}{\left(\frac{\pi}{4} + 28 \right)} + 1\right)^{2}}{\left(1 + \cot^{2}{\left(\frac{\pi}{4} + 28 \right)}\right)^{2}} + \frac{\left(- \cot^{2}{\left(\frac{\pi}{4} + 62 \right)} + 1\right)^{2}}{\left(1 + \cot^{2}{\left(\frac{\pi}{4} + 62 \right)}\right)^{2}} + 1\right)}$$
___
-4 - 2*\/ 3
--------------------------------------------------------------------------------
/ 2\ / 4 2 4 2 \
| / ___\ | | 16*sin (28)*sin (56) 16*sin (62)*sin (124) |
2*\1 + \-2 - \/ 3 / /*|1 + ------------------------ + -------------------------|
| 2 2|
| / 2 4 \ / 2 4 \ |
\ \sin (56) + 4*sin (28)/ \sin (124) + 4*sin (62)/ /
$$\frac{-4 - 2 \sqrt{3}}{2 \cdot \left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(\frac{16 \sin^{4}{\left(28 \right)} \sin^{2}{\left(56 \right)}}{\left(4 \sin^{4}{\left(28 \right)} + \sin^{2}{\left(56 \right)}\right)^{2}} + \frac{16 \sin^{4}{\left(62 \right)} \sin^{2}{\left(124 \right)}}{\left(\sin^{2}{\left(124 \right)} + 4 \sin^{4}{\left(62 \right)}\right)^{2}} + 1\right)}$$
___
-4 + 2*\/ 3
-----------------------------------------------------------------------------------
/ 2\ / 2 2 \
| / ___\ | | sin (56) sin (124) |
2*\1 + \-2 + \/ 3 / /*|1 + -------------------------- + --------------------------|
| 2 2 |
| / 2 \ / 2 \ |
| | sin (56) | 4 | sin (124) | 4 |
| |1 + ----------| *sin (28) |1 + ----------| *sin (62)|
| | 4 | | 4 | |
\ \ 4*sin (28)/ \ 4*sin (62)/ /
$$\frac{-4 + 2 \sqrt{3}}{2 \left(\left(-2 + \sqrt{3}\right)^{2} + 1\right) \left(\frac{\sin^{2}{\left(56 \right)}}{\left(1 + \frac{\sin^{2}{\left(56 \right)}}{4 \sin^{4}{\left(28 \right)}}\right)^{2} \sin^{4}{\left(28 \right)}} + \frac{\sin^{2}{\left(124 \right)}}{\left(\frac{\sin^{2}{\left(124 \right)}}{4 \sin^{4}{\left(62 \right)}} + 1\right)^{2} \sin^{4}{\left(62 \right)}} + 1\right)}$$
___
-4 - 2*\/ 3
------------------------------------------------------------------------------------
/ 2\ / 4 4 \
| / ___\ | | 16*sin (28) 16*sin (62) |
2*\1 + \-2 - \/ 3 / /*|1 + -------------------------- + ---------------------------|
| 2 2 |
| / 4 \ / 4 \ |
| | 4*sin (28)| 2 | 4*sin (62)| 2 |
| |1 + ----------| *sin (56) |1 + ----------| *sin (124)|
| | 2 | | 2 | |
\ \ sin (56) / \ sin (124) / /
$$\frac{-4 - 2 \sqrt{3}}{2 \cdot \left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(\frac{16 \sin^{4}{\left(28 \right)}}{\left(\frac{4 \sin^{4}{\left(28 \right)}}{\sin^{2}{\left(56 \right)}} + 1\right)^{2} \sin^{2}{\left(56 \right)}} + \frac{16 \sin^{4}{\left(62 \right)}}{\left(1 + \frac{4 \sin^{4}{\left(62 \right)}}{\sin^{2}{\left(124 \right)}}\right)^{2} \sin^{2}{\left(124 \right)}} + 1\right)}$$
___
-4 + 2*\/ 3
-------------------------------------------------------------------------------------------------------
/ 2\ / 2 2 \
| / ___\ | | 4*csc (28) 4*csc (62) |
2*\1 + \-2 + \/ 3 / /*|1 + ------------------------------------ + ------------------------------------|
| 2 2 |
| / 2 \ / 2 \ |
| | csc (28) | 2/ pi\ | csc (62) | 2/ pi\|
| |1 + --------------| *csc |-28 + --| |1 + --------------| *csc |-62 + --||
| | 2/ pi\| \ 2 / | 2/ pi\| \ 2 /|
| | csc |-28 + --|| | csc |-62 + --|| |
\ \ \ 2 // \ \ 2 // /
$$\frac{-4 + 2 \sqrt{3}}{2 \left(\left(-2 + \sqrt{3}\right)^{2} + 1\right) \left(\frac{4 \csc^{2}{\left(28 \right)}}{\left(1 + \frac{\csc^{2}{\left(28 \right)}}{\csc^{2}{\left(-28 + \frac{\pi}{2} \right)}}\right)^{2} \csc^{2}{\left(-28 + \frac{\pi}{2} \right)}} + \frac{4 \csc^{2}{\left(62 \right)}}{\left(\frac{\csc^{2}{\left(62 \right)}}{\csc^{2}{\left(-62 + \frac{\pi}{2} \right)}} + 1\right)^{2} \csc^{2}{\left(-62 + \frac{\pi}{2} \right)}} + 1\right)}$$
___
-4 + 2*\/ 3
-----------------------------------------------------------------------------------------
/ 2/ pi\ 2/ pi\ \
/ 2\ | 4*sec |28 - --| 4*sec |62 - --| |
| / ___\ | | \ 2 / \ 2 / |
2*\1 + \-2 + \/ 3 / /*|1 + ----------------------------- + -----------------------------|
| 2 2 |
| / 2/ pi\\ / 2/ pi\\ |
| | sec |28 - --|| | sec |62 - --|| |
| | \ 2 /| 2 | \ 2 /| 2 |
| |1 + -------------| *sec (28) |1 + -------------| *sec (62)|
| | 2 | | 2 | |
\ \ sec (28) / \ sec (62) / /
$$\frac{-4 + 2 \sqrt{3}}{2 \left(\left(-2 + \sqrt{3}\right)^{2} + 1\right) \left(\frac{4 \sec^{2}{\left(- \frac{\pi}{2} + 28 \right)}}{\left(1 + \frac{\sec^{2}{\left(- \frac{\pi}{2} + 28 \right)}}{\sec^{2}{\left(28 \right)}}\right)^{2} \sec^{2}{\left(28 \right)}} + \frac{4 \sec^{2}{\left(- \frac{\pi}{2} + 62 \right)}}{\left(\frac{\sec^{2}{\left(- \frac{\pi}{2} + 62 \right)}}{\sec^{2}{\left(62 \right)}} + 1\right)^{2} \sec^{2}{\left(62 \right)}} + 1\right)}$$
___
-4 + 2*\/ 3
---------------------------------------------------------------------------------------------------
/ 2\ / 2 2 \
| / ___\ | | 4*cos (28) 4*cos (62) |
2*\1 + \-2 + \/ 3 / /*|1 + ---------------------------------- + ----------------------------------|
| 2 2 |
| / 2 \ / 2 \ |
| | cos (28) | 2/ pi\ | cos (62) | 2/ pi\|
| |1 + -------------| *cos |28 - --| |1 + -------------| *cos |62 - --||
| | 2/ pi\| \ 2 / | 2/ pi\| \ 2 /|
| | cos |28 - --|| | cos |62 - --|| |
\ \ \ 2 // \ \ 2 // /
$$\frac{-4 + 2 \sqrt{3}}{2 \left(\left(-2 + \sqrt{3}\right)^{2} + 1\right) \left(\frac{4 \cos^{2}{\left(28 \right)}}{\left(1 + \frac{\cos^{2}{\left(28 \right)}}{\cos^{2}{\left(- \frac{\pi}{2} + 28 \right)}}\right)^{2} \cos^{2}{\left(- \frac{\pi}{2} + 28 \right)}} + \frac{4 \cos^{2}{\left(62 \right)}}{\left(\frac{\cos^{2}{\left(62 \right)}}{\cos^{2}{\left(- \frac{\pi}{2} + 62 \right)}} + 1\right)^{2} \cos^{2}{\left(- \frac{\pi}{2} + 62 \right)}} + 1\right)}$$
___
-4 - 2*\/ 3
-------------------------------------------------------------------------------------------
/ 2/ pi\ 2/ pi\ \
/ 2\ | 4*csc |-28 + --| 4*csc |-62 + --| |
| / ___\ | | \ 2 / \ 2 / |
2*\1 + \-2 - \/ 3 / /*|1 + ------------------------------ + ------------------------------|
| 2 2 |
| / 2/ pi\\ / 2/ pi\\ |
| | csc |-28 + --|| | csc |-62 + --|| |
| | \ 2 /| 2 | \ 2 /| 2 |
| |1 + --------------| *csc (28) |1 + --------------| *csc (62)|
| | 2 | | 2 | |
\ \ csc (28) / \ csc (62) / /
$$\frac{-4 - 2 \sqrt{3}}{2 \cdot \left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(\frac{4 \csc^{2}{\left(-28 + \frac{\pi}{2} \right)}}{\left(\frac{\csc^{2}{\left(-28 + \frac{\pi}{2} \right)}}{\csc^{2}{\left(28 \right)}} + 1\right)^{2} \csc^{2}{\left(28 \right)}} + \frac{4 \csc^{2}{\left(-62 + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(-62 + \frac{\pi}{2} \right)}}{\csc^{2}{\left(62 \right)}}\right)^{2} \csc^{2}{\left(62 \right)}} + 1\right)}$$
___
-4 - 2*\/ 3
-----------------------------------------------------------------------------------------
/ 2/ pi\ 2/ pi\ \
/ 2\ | 4*cos |28 - --| 4*cos |62 - --| |
| / ___\ | | \ 2 / \ 2 / |
2*\1 + \-2 - \/ 3 / /*|1 + ----------------------------- + -----------------------------|
| 2 2 |
| / 2/ pi\\ / 2/ pi\\ |
| | cos |28 - --|| | cos |62 - --|| |
| | \ 2 /| 2 | \ 2 /| 2 |
| |1 + -------------| *cos (28) |1 + -------------| *cos (62)|
| | 2 | | 2 | |
\ \ cos (28) / \ cos (62) / /
$$\frac{-4 - 2 \sqrt{3}}{2 \cdot \left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(\frac{4 \cos^{2}{\left(- \frac{\pi}{2} + 28 \right)}}{\left(\frac{\cos^{2}{\left(- \frac{\pi}{2} + 28 \right)}}{\cos^{2}{\left(28 \right)}} + 1\right)^{2} \cos^{2}{\left(28 \right)}} + \frac{4 \cos^{2}{\left(- \frac{\pi}{2} + 62 \right)}}{\left(1 + \frac{\cos^{2}{\left(- \frac{\pi}{2} + 62 \right)}}{\cos^{2}{\left(62 \right)}}\right)^{2} \cos^{2}{\left(62 \right)}} + 1\right)}$$
___
-4 - 2*\/ 3
---------------------------------------------------------------------------------------------------
/ 2\ / 2 2 \
| / ___\ | | 4*sec (28) 4*sec (62) |
2*\1 + \-2 - \/ 3 / /*|1 + ---------------------------------- + ----------------------------------|
| 2 2 |
| / 2 \ / 2 \ |
| | sec (28) | 2/ pi\ | sec (62) | 2/ pi\|
| |1 + -------------| *sec |28 - --| |1 + -------------| *sec |62 - --||
| | 2/ pi\| \ 2 / | 2/ pi\| \ 2 /|
| | sec |28 - --|| | sec |62 - --|| |
\ \ \ 2 // \ \ 2 // /
$$\frac{-4 - 2 \sqrt{3}}{2 \cdot \left(1 + \left(-2 - \sqrt{3}\right)^{2}\right) \left(\frac{4 \sec^{2}{\left(28 \right)}}{\left(\frac{\sec^{2}{\left(28 \right)}}{\sec^{2}{\left(- \frac{\pi}{2} + 28 \right)}} + 1\right)^{2} \sec^{2}{\left(- \frac{\pi}{2} + 28 \right)}} + \frac{4 \sec^{2}{\left(62 \right)}}{\left(1 + \frac{\sec^{2}{\left(62 \right)}}{\sec^{2}{\left(- \frac{\pi}{2} + 62 \right)}}\right)^{2} \sec^{2}{\left(- \frac{\pi}{2} + 62 \right)}} + 1\right)}$$
(-4 - 2*sqrt(3))/(2*(1 + (-2 - sqrt(3))^2)*(1 + 4*sec(28)^2/((1 + sec(28)^2/sec(28 - pi/2)^2)^2*sec(28 - pi/2)^2) + 4*sec(62)^2/((1 + sec(62)^2/sec(62 - pi/2)^2)^2*sec(62 - pi/2)^2)))