Господин Экзамен
Общий знаменатель sin(10*x)/20-sin(14*x)/28
Решение
Вы ввели
[src]
sin(10*x) sin(14*x)
--------- - ---------
20 28
$$\frac{\sin{\left(10 x \right)}}{20} - \frac{\sin{\left(14 x \right)}}{28}$$
sin(10*x)/20 - sin(14*x)/28
Численный ответ
[src]
0.05*sin(10*x) - 0.0357142857142857*sin(14*x)
0.05*sin(10*x) - 0.0357142857142857*sin(14*x)
Рациональный знаменатель
[src]
-20*sin(14*x) + 28*sin(10*x)
----------------------------
560
$$\frac{28 \sin{\left(10 x \right)} - 20 \sin{\left(14 x \right)}}{560}$$
(-20*sin(14*x) + 28*sin(10*x))/560
Степени
[src]
/ -10*I*x 10*I*x\ / -14*I*x 14*I*x\
I*\- e + e / I*\- e + e /
- ------------------------ + ------------------------
40 56
$$- \frac{i \left(e^{10 i x} - e^{- 10 i x}\right)}{40} + \frac{i \left(e^{14 i x} - e^{- 14 i x}\right)}{56}$$
-i*(-exp(-10*i*x) + exp(10*i*x))/40 + i*(-exp(-14*i*x) + exp(14*i*x))/56
Объединение рациональных выражений
[src]
-5*sin(14*x) + 7*sin(10*x)
--------------------------
140
$$\frac{7 \sin{\left(10 x \right)} - 5 \sin{\left(14 x \right)}}{140}$$
(-5*sin(14*x) + 7*sin(10*x))/140
Тригонометрическая часть
[src]
1 1 - ------------ + ------------ 28*csc(14*x) 20*csc(10*x)
$$- \frac{1}{28 \csc{\left(14 x \right)}} + \frac{1}{20 \csc{\left(10 x \right)}}$$
1 1 - ----------------- + ----------------- 28*csc(pi - 14*x) 20*csc(pi - 10*x)
$$\frac{1}{20 \csc{\left(- 10 x + \pi \right)}} - \frac{1}{28 \csc{\left(- 14 x + \pi \right)}}$$
/ pi\ / pi\
cos|14*x - --| cos|10*x - --|
\ 2 / \ 2 /
- -------------- + --------------
28 20
$$\frac{\cos{\left(10 x - \frac{\pi}{2} \right)}}{20} - \frac{\cos{\left(14 x - \frac{\pi}{2} \right)}}{28}$$
1 1
- ----------------- + -----------------
/ pi\ / pi\
28*sec|14*x - --| 20*sec|10*x - --|
\ 2 / \ 2 /
$$- \frac{1}{28 \sec{\left(14 x - \frac{\pi}{2} \right)}} + \frac{1}{20 \sec{\left(10 x - \frac{\pi}{2} \right)}}$$
1 1
- ----------------- + -----------------
/pi \ /pi \
28*sec|-- - 14*x| 20*sec|-- - 10*x|
\2 / \2 /
$$\frac{1}{20 \sec{\left(- 10 x + \frac{\pi}{2} \right)}} - \frac{1}{28 \sec{\left(- 14 x + \frac{\pi}{2} \right)}}$$
cos(7*x)*sin(7*x) cos(5*x)*sin(5*x)
- ----------------- + -----------------
14 10
$$\frac{\sin{\left(5 x \right)} \cos{\left(5 x \right)}}{10} - \frac{\sin{\left(7 x \right)} \cos{\left(7 x \right)}}{14}$$
cot(7*x) cot(5*x)
- ------------------ + ------------------
/ 2 \ / 2 \
14*\1 + cot (7*x)/ 10*\1 + cot (5*x)/
$$- \frac{\cot{\left(7 x \right)}}{14 \left(\cot^{2}{\left(7 x \right)} + 1\right)} + \frac{\cot{\left(5 x \right)}}{10 \left(\cot^{2}{\left(5 x \right)} + 1\right)}$$
tan(7*x) tan(5*x)
- ------------------ + ------------------
/ 2 \ / 2 \
14*\1 + tan (7*x)/ 10*\1 + tan (5*x)/
$$- \frac{\tan{\left(7 x \right)}}{14 \left(\tan^{2}{\left(7 x \right)} + 1\right)} + \frac{\tan{\left(5 x \right)}}{10 \left(\tan^{2}{\left(5 x \right)} + 1\right)}$$
1 1
- --------------------------- + ---------------------------
/ 1 \ / 1 \
14*|1 + ---------|*cot(7*x) 10*|1 + ---------|*cot(5*x)
| 2 | | 2 |
\ cot (7*x)/ \ cot (5*x)/
$$- \frac{1}{14 \cdot \left(1 + \frac{1}{\cot^{2}{\left(7 x \right)}}\right) \cot{\left(7 x \right)}} + \frac{1}{10 \cdot \left(1 + \frac{1}{\cot^{2}{\left(5 x \right)}}\right) \cot{\left(5 x \right)}}$$
/ 2/ pi\\ / 2/ pi\\
|1 - cot |7*x + --||*(1 + sin(14*x)) |1 - cot |5*x + --||*(1 + sin(10*x))
\ \ 4 // \ \ 4 //
- ------------------------------------ + ------------------------------------
56 40
$$\frac{\left(- \cot^{2}{\left(5 x + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(10 x \right)} + 1\right)}{40} - \frac{\left(- \cot^{2}{\left(7 x + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(14 x \right)} + 1\right)}{56}$$
2/ pi\ 2/ pi\
-1 + tan |7*x + --| -1 + tan |5*x + --|
\ 4 / \ 4 /
- ----------------------- + -----------------------
/ 2/ pi\\ / 2/ pi\\
28*|1 + tan |7*x + --|| 20*|1 + tan |5*x + --||
\ \ 4 // \ \ 4 //
$$\frac{\tan^{2}{\left(5 x + \frac{\pi}{4} \right)} - 1}{20 \left(\tan^{2}{\left(5 x + \frac{\pi}{4} \right)} + 1\right)} - \frac{\tan^{2}{\left(7 x + \frac{\pi}{4} \right)} - 1}{28 \left(\tan^{2}{\left(7 x + \frac{\pi}{4} \right)} + 1\right)}$$
2/ pi\ 2/ pi\
1 - cot |7*x + --| 1 - cot |5*x + --|
\ 4 / \ 4 /
- ----------------------- + -----------------------
/ 2/ pi\\ / 2/ pi\\
28*|1 + cot |7*x + --|| 20*|1 + cot |5*x + --||
\ \ 4 // \ \ 4 //
$$\frac{- \cot^{2}{\left(5 x + \frac{\pi}{4} \right)} + 1}{20 \left(\cot^{2}{\left(5 x + \frac{\pi}{4} \right)} + 1\right)} - \frac{- \cot^{2}{\left(7 x + \frac{\pi}{4} \right)} + 1}{28 \left(\cot^{2}{\left(7 x + \frac{\pi}{4} \right)} + 1\right)}$$
/ 0 for 14*x mod pi = 0 / 0 for 10*x mod pi = 0
< <
\sin(14*x) otherwise \sin(10*x) otherwise
- ------------------------------- + -------------------------------
28 20
$$\left(\frac{\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\sin{\left(10 x \right)} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\sin{\left(14 x \right)} & \text{otherwise} \end{cases}}{28}\right)$$
/ 0 for 14*x mod pi = 0 / 0 for 10*x mod pi = 0
| |
< 1 < 1
|--------- otherwise |--------- otherwise
\csc(14*x) \csc(10*x)
- ------------------------------- + -------------------------------
28 20
$$\left(\frac{\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\frac{1}{\csc{\left(10 x \right)}} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\frac{1}{\csc{\left(14 x \right)}} & \text{otherwise} \end{cases}}{28}\right)$$
/ 0 for 14*x mod pi = 0 / 0 for 10*x mod pi = 0
| |
< / pi\ < / pi\
|cos|14*x - --| otherwise |cos|10*x - --| otherwise
\ \ 2 / \ \ 2 /
- ------------------------------------ + ------------------------------------
28 20
$$\left(\frac{\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\cos{\left(10 x - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\cos{\left(14 x - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}}{28}\right)$$
2 2
sin (7*x) sin (5*x)
- ----------------------------- + -----------------------------
/ 4 \ / 4 \
| 4*sin (7*x)| | 4*sin (5*x)|
7*|1 + -----------|*sin(14*x) 5*|1 + -----------|*sin(10*x)
| 2 | | 2 |
\ sin (14*x)/ \ sin (10*x)/
$$- \frac{\sin^{2}{\left(7 x \right)}}{7 \cdot \left(\frac{4 \sin^{4}{\left(7 x \right)}}{\sin^{2}{\left(14 x \right)}} + 1\right) \sin{\left(14 x \right)}} + \frac{\sin^{2}{\left(5 x \right)}}{5 \cdot \left(\frac{4 \sin^{4}{\left(5 x \right)}}{\sin^{2}{\left(10 x \right)}} + 1\right) \sin{\left(10 x \right)}}$$
/ 0 for 14*x mod pi = 0 / 0 for 10*x mod pi = 0
| |
| 1 | 1
<-------------- otherwise <-------------- otherwise
| / pi\ | / pi\
|sec|14*x - --| |sec|10*x - --|
\ \ 2 / \ \ 2 /
- ------------------------------------ + ------------------------------------
28 20
$$\left(\frac{\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\frac{1}{\sec{\left(10 x - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\frac{1}{\sec{\left(14 x - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}}{28}\right)$$
/ / 3*pi\ / / 3*pi\
| 1 for |14*x + ----| mod 2*pi = 0 | 1 for |10*x + ----| mod 2*pi = 0
< \ 2 / < \ 2 /
| |
\sin(14*x) otherwise \sin(10*x) otherwise
- ------------------------------------------ + ------------------------------------------
28 20
$$\left(\frac{\begin{cases} 1 & \text{for}\: \left(10 x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(10 x \right)} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 1 & \text{for}\: \left(14 x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(14 x \right)} & \text{otherwise} \end{cases}}{28}\right)$$
sec(7*x) sec(5*x)
- ------------------------------------- + -------------------------------------
/ 2 \ / 2 \
| sec (7*x) | / pi\ | sec (5*x) | / pi\
14*|1 + --------------|*sec|7*x - --| 10*|1 + --------------|*sec|5*x - --|
| 2/ pi\| \ 2 / | 2/ pi\| \ 2 /
| sec |7*x - --|| | sec |5*x - --||
\ \ 2 // \ \ 2 //
$$- \frac{\sec{\left(7 x \right)}}{14 \left(\frac{\sec^{2}{\left(7 x \right)}}{\sec^{2}{\left(7 x - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(7 x - \frac{\pi}{2} \right)}} + \frac{\sec{\left(5 x \right)}}{10 \left(\frac{\sec^{2}{\left(5 x \right)}}{\sec^{2}{\left(5 x - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(5 x - \frac{\pi}{2} \right)}}$$
/ 0 for 14*x mod pi = 0 / 0 for 10*x mod pi = 0
| |
| 2*cot(7*x) | 2*cot(5*x)
<------------- otherwise <------------- otherwise
| 2 | 2
|1 + cot (7*x) |1 + cot (5*x)
\ \
- ----------------------------------- + -----------------------------------
28 20
$$\left(\frac{\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\frac{2 \cot{\left(5 x \right)}}{\cot^{2}{\left(5 x \right)} + 1} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\frac{2 \cot{\left(7 x \right)}}{\cot^{2}{\left(7 x \right)} + 1} & \text{otherwise} \end{cases}}{28}\right)$$
/ 0 for 14*x mod pi = 0 / 0 for 10*x mod pi = 0
| |
| 2*tan(7*x) | 2*tan(5*x)
<------------- otherwise <------------- otherwise
| 2 | 2
|1 + tan (7*x) |1 + tan (5*x)
\ \
- ----------------------------------- + -----------------------------------
28 20
$$\left(\frac{\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\frac{2 \tan{\left(5 x \right)}}{\tan^{2}{\left(5 x \right)} + 1} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\frac{2 \tan{\left(7 x \right)}}{\tan^{2}{\left(7 x \right)} + 1} & \text{otherwise} \end{cases}}{28}\right)$$
/ pi\ / pi\
cos|7*x - --| cos|5*x - --|
\ 2 / \ 2 /
- -------------------------------- + --------------------------------
/ 2/ pi\\ / 2/ pi\\
| cos |7*x - --|| | cos |5*x - --||
| \ 2 /| | \ 2 /|
14*|1 + --------------|*cos(7*x) 10*|1 + --------------|*cos(5*x)
| 2 | | 2 |
\ cos (7*x) / \ cos (5*x) /
$$- \frac{\cos{\left(7 x - \frac{\pi}{2} \right)}}{14 \cdot \left(1 + \frac{\cos^{2}{\left(7 x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(7 x \right)}}\right) \cos{\left(7 x \right)}} + \frac{\cos{\left(5 x - \frac{\pi}{2} \right)}}{10 \cdot \left(1 + \frac{\cos^{2}{\left(5 x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(5 x \right)}}\right) \cos{\left(5 x \right)}}$$
/pi \ /pi \
csc|-- - 7*x| csc|-- - 5*x|
\2 / \2 /
- -------------------------------- + --------------------------------
/ 2/pi \\ / 2/pi \\
| csc |-- - 7*x|| | csc |-- - 5*x||
| \2 /| | \2 /|
14*|1 + --------------|*csc(7*x) 10*|1 + --------------|*csc(5*x)
| 2 | | 2 |
\ csc (7*x) / \ csc (5*x) /
$$- \frac{\csc{\left(- 7 x + \frac{\pi}{2} \right)}}{14 \cdot \left(1 + \frac{\csc^{2}{\left(- 7 x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(7 x \right)}}\right) \csc{\left(7 x \right)}} + \frac{\csc{\left(- 5 x + \frac{\pi}{2} \right)}}{10 \cdot \left(1 + \frac{\csc^{2}{\left(- 5 x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(5 x \right)}}\right) \csc{\left(5 x \right)}}$$
/ 0 for 14*x mod pi = 0 / 0 for 10*x mod pi = 0
| |
| 2 | 2
|------------------------ otherwise |------------------------ otherwise
$$\left(\frac{\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(5 x \right)}}\right) \tan{\left(5 x \right)}} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(7 x \right)}}\right) \tan{\left(7 x \right)}} & \text{otherwise} \end{cases}}{28}\right)$$
/ 0 for 14*x mod pi = 0 / 0 for 10*x mod pi = 0
| |
$$\left(\frac{\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\sin{\left(10 x \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\sin{\left(14 x \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}}{28}\right)$$
/ / 3*pi\ / / 3*pi\
| 1 for |14*x + ----| mod 2*pi = 0 | 1 for |10*x + ----| mod 2*pi = 0
| \ 2 / | \ 2 /
| |
| 2/ pi\ | 2/ pi\
<-1 + tan |7*x + --| <-1 + tan |5*x + --|
| \ 4 / | \ 4 /
|------------------- otherwise |------------------- otherwise
| 2/ pi\ | 2/ pi\
| 1 + tan |7*x + --| | 1 + tan |5*x + --|
\ \ 4 / \ \ 4 /
- ---------------------------------------------------- + ----------------------------------------------------
28 20
$$\left(\frac{\begin{cases} 1 & \text{for}\: \left(10 x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(5 x + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(5 x + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 1 & \text{for}\: \left(14 x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(7 x + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(7 x + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}}{28}\right)$$
/ 0 for 14*x mod pi = 0 / 0 for 10*x mod pi = 0
| |
| sin(14*x) | sin(10*x)
|--------------------------- otherwise |--------------------------- otherwise
$$\left(\frac{\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\frac{\sin{\left(10 x \right)}}{\left(1 + \frac{\sin^{2}{\left(10 x \right)}}{4 \sin^{4}{\left(5 x \right)}}\right) \sin^{2}{\left(5 x \right)}} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\frac{\sin{\left(14 x \right)}}{\left(1 + \frac{\sin^{2}{\left(14 x \right)}}{4 \sin^{4}{\left(7 x \right)}}\right) \sin^{2}{\left(7 x \right)}} & \text{otherwise} \end{cases}}{28}\right)$$
/ 0 for 14*x mod pi = 0 / 0 for 10*x mod pi = 0
| |
|/ 0 for 14*x mod pi = 0 |/ 0 for 10*x mod pi = 0
|| ||
<| 2*cot(7*x) <| 2*cot(5*x)
|<------------- otherwise otherwise |<------------- otherwise otherwise
|| 2 || 2
||1 + cot (7*x) ||1 + cot (5*x)
\\ \\
- --------------------------------------------------------- + ---------------------------------------------------------
28 20
$$\left(\frac{\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\frac{2 \cot{\left(5 x \right)}}{\cot^{2}{\left(5 x \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\frac{2 \cot{\left(7 x \right)}}{\cot^{2}{\left(7 x \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}}{28}\right)$$
/ 0 for 14*x mod pi = 0 / 0 for 10*x mod pi = 0
| |
| / pi\ | / pi\
| 2*sec|7*x - --| | 2*sec|5*x - --|
| \ 2 / | \ 2 /
|----------------------------- otherwise |----------------------------- otherwise
$$\left(\frac{\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\frac{2 \sec{\left(5 x - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(5 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(5 x \right)}}\right) \sec{\left(5 x \right)}} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\frac{2 \sec{\left(7 x - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(7 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(7 x \right)}}\right) \sec{\left(7 x \right)}} & \text{otherwise} \end{cases}}{28}\right)$$
/ 0 for 14*x mod pi = 0 / 0 for 10*x mod pi = 0
| |
| 2*cos(7*x) | 2*cos(5*x)
|---------------------------------- otherwise |---------------------------------- otherwise
|/ 2 \ |/ 2 \
<| cos (7*x) | / pi\ <| cos (5*x) | / pi\
||1 + --------------|*cos|7*x - --| ||1 + --------------|*cos|5*x - --|
|| 2/ pi\| \ 2 / || 2/ pi\| \ 2 /
|| cos |7*x - --|| || cos |5*x - --||
|\ \ 2 // |\ \ 2 //
\ \
- -------------------------------------------------------- + --------------------------------------------------------
28 20
$$\left(\frac{\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\frac{2 \cos{\left(5 x \right)}}{\left(\frac{\cos^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(5 x - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\frac{2 \cos{\left(7 x \right)}}{\left(\frac{\cos^{2}{\left(7 x \right)}}{\cos^{2}{\left(7 x - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(7 x - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}}{28}\right)$$
/ 0 for 14*x mod pi = 0 / 0 for 10*x mod pi = 0
| |
| 2*csc(7*x) | 2*csc(5*x)
|---------------------------------- otherwise |---------------------------------- otherwise
|/ 2 \ |/ 2 \
<| csc (7*x) | /pi \ <| csc (5*x) | /pi \
||1 + --------------|*csc|-- - 7*x| ||1 + --------------|*csc|-- - 5*x|
|| 2/pi \| \2 / || 2/pi \| \2 /
|| csc |-- - 7*x|| || csc |-- - 5*x||
|\ \2 // |\ \2 //
\ \
- -------------------------------------------------------- + --------------------------------------------------------
28 20
$$\left(\frac{\begin{cases} 0 & \text{for}\: 10 x \bmod \pi = 0 \\\frac{2 \csc{\left(5 x \right)}}{\left(\frac{\csc^{2}{\left(5 x \right)}}{\csc^{2}{\left(- 5 x + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- 5 x + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}}{20}\right) - \left(\frac{\begin{cases} 0 & \text{for}\: 14 x \bmod \pi = 0 \\\frac{2 \csc{\left(7 x \right)}}{\left(\frac{\csc^{2}{\left(7 x \right)}}{\csc^{2}{\left(- 7 x + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- 7 x + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}}{28}\right)$$
-Piecewise((0, Mod(14*x = pi, 0)), (2*csc(7*x)/((1 + csc(7*x)^2/csc(pi/2 - 7*x)^2)*csc(pi/2 - 7*x)), True))/28 + Piecewise((0, Mod(10*x = pi, 0)), (2*csc(5*x)/((1 + csc(5*x)^2/csc(pi/2 - 5*x)^2)*csc(pi/2 - 5*x)), True))/20