Господин Экзамен

Lang:

Другие калькуляторы

Как пользоваться?
sin(7*x)+sin(3*x) если x=-1/3
y9*y6 если y9=-2
(c+4)*(4+c) если c=3
k^2-6*k+9*k если k=3/2
Разложить многочлен на множители:
144-y^2/12-y
u*z^8+u*y^8-y*z^8-y9
x^4+4
x^8+1
Общий знаменатель:
(b+2)/15*b-(3*c-5)/45*c
((c+5)/(5*c-1)+(c+5)/(c+1))/(c^2+5*c)/(1-5*c)+(c^2+5)/c+1
(c-d)/c*(c/(c-d)+c/d)
asin(2*x-1)/8+(x*sqrt(x-x^2))/2-sqrt(x-x^2)/4
Умножение столбиком:
64*84
81*45
92*46
96*18
Деление столбиком:
8760/6
21788/6
167/7
359/8
Раскрыть скобки в:
(b-8)^2-2*b*(7*b-8)
(10*p-7*g)*(7*g+10*p)
x^2-c^2+(c-x)*(c+x)
a*(m-b)+b-m
Разложение числа на простые множители:
8402
5996
705
37037
Производная:
-1/3
Интеграл d{x}:
-1/3
Идентичные выражения
sin(семь *x)+sin(три *x) если x=- один / три
синус от (7 умножить на x) плюс синус от (3 умножить на x) если x равно минус 1 делить на 3
синус от (семь умножить на x) плюс синус от (три умножить на x) если x равно минус один делить на три
sin(7x)+sin(3x) если x=-1/3
sin7x+sin3x если x=-1/3
sin(7*x)+sin(3*x) при x=-1/3
sin(7*x)+sin(3*x) если x=-1 разделить на 3
Похожие выражения
sin(7*x)-sin(3*x) если x=-1/3
sin(7*x)+sin(3*x) если x=+1/3

Упрощение выражений/ sin(7*x)+sin(3*x) если x=-1/3

sin(7x)+sin(3x) если x=-1/3

Решение

Вы ввели [src]

sin(7*x) + sin(3*x)

$$\sin{\left(3 x \right)} + \sin{\left(7 x \right)}$$

sin(7*x) + sin(3*x)

Подстановка условия [src]

sin(7*x) + sin(3*x) при x = -1/3

подставляем

sin(7*x) + sin(3*x)

$$\sin{\left(3 x \right)} + \sin{\left(7 x \right)}$$

sin(3*x) + sin(7*x)

$$\sin{\left(3 x \right)} + \sin{\left(7 x \right)}$$

переменные

x = -1/3

$$x = - \frac{1}{3}$$

sin(3*(-1/3)) + sin(7*(-1/3))

$$\sin{\left(3 (-1/3) \right)} + \sin{\left(7 (-1/3) \right)}$$

-sin(1) - sin(7/3)

$$- \sin{\left(1 \right)} - \sin{\left(\frac{7}{3} \right)}$$

-sin(1) - sin(7/3)

Численный ответ [src]

sin(3*x) + sin(7*x)

sin(3*x) + sin(7*x)

Степени [src]

    /   -7*I*x    7*I*x\     /   -3*I*x    3*I*x\
  I*\- e       + e     /   I*\- e       + e     /
- ---------------------- - ----------------------
            2                        2

$$- \frac{i \left(e^{3 i x} - e^{- 3 i x}\right)}{2} - \frac{i \left(e^{7 i x} - e^{- 7 i x}\right)}{2}$$

-i*(-exp(-7*i*x) + exp(7*i*x))/2 - i*(-exp(-3*i*x) + exp(3*i*x))/2

Раскрыть выражение [src]

        7            3                         5   
- 64*sin (x) - 60*sin (x) + 10*sin(x) + 112*sin (x)

$$- 64 \sin^{7}{\left(x \right)} + 112 \sin^{5}{\left(x \right)} - 60 \sin^{3}{\left(x \right)} + 10 \sin{\left(x \right)}$$

     3         7            4       3           2                  6                   2       5   
- sin (x) - sin (x) - 35*cos (x)*sin (x) + 3*cos (x)*sin(x) + 7*cos (x)*sin(x) + 21*cos (x)*sin (x)

$$- \sin^{7}{\left(x \right)} + 21 \sin^{5}{\left(x \right)} \cos^{2}{\left(x \right)} - 35 \sin^{3}{\left(x \right)} \cos^{4}{\left(x \right)} + 7 \sin{\left(x \right)} \cos^{6}{\left(x \right)} - \sin^{3}{\left(x \right)} + 3 \sin{\left(x \right)} \cos^{2}{\left(x \right)}$$

-sin(x)^3 - sin(x)^7 - 35*cos(x)^4*sin(x)^3 + 3*cos(x)^2*sin(x) + 7*cos(x)^6*sin(x) + 21*cos(x)^2*sin(x)^5

Тригонометрическая часть [src]

2*cos(2*x)*sin(5*x)

$$2 \sin{\left(5 x \right)} \cos{\left(2 x \right)}$$

   1          1    
-------- + --------
csc(3*x)   csc(7*x)

$$\frac{1}{\csc{\left(7 x \right)}} + \frac{1}{\csc{\left(3 x \right)}}$$

   /      pi\      /      pi\
cos|3*x - --| + cos|7*x - --|
   \      2 /      \      2 /

$$\cos{\left(3 x - \frac{\pi}{2} \right)} + \cos{\left(7 x - \frac{\pi}{2} \right)}$$

      1               1      
------------- + -------------
csc(pi - 7*x)   csc(pi - 3*x)

$$\frac{1}{\csc{\left(- 3 x + \pi \right)}} + \frac{1}{\csc{\left(- 7 x + \pi \right)}}$$

      1               1      
------------- + -------------
   /      pi\      /      pi\
sec|3*x - --|   sec|7*x - --|
   \      2 /      \      2 /

$$\frac{1}{\sec{\left(7 x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(3 x - \frac{\pi}{2} \right)}}$$

      1               1      
------------- + -------------
   /pi      \      /pi      \
sec|-- - 7*x|   sec|-- - 3*x|
   \2       /      \2       /

$$\frac{1}{\sec{\left(- 3 x + \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(- 7 x + \frac{\pi}{2} \right)}}$$

                  /3*x\                     /7*x\
(1 + cos(3*x))*tan|---| + (1 + cos(7*x))*tan|---|
                  \ 2 /                     \ 2 /

$$\left(\cos{\left(3 x \right)} + 1\right) \tan{\left(\frac{3 x}{2} \right)} + \left(\cos{\left(7 x \right)} + 1\right) \tan{\left(\frac{7 x}{2} \right)}$$

       /3*x\           /7*x\ 
  2*cot|---|      2*cot|---| 
       \ 2 /           \ 2 / 
------------- + -------------
       2/3*x\          2/7*x\
1 + cot |---|   1 + cot |---|
        \ 2 /           \ 2 /

$$\frac{2 \cot{\left(\frac{7 x}{2} \right)}}{\cot^{2}{\left(\frac{7 x}{2} \right)} + 1} + \frac{2 \cot{\left(\frac{3 x}{2} \right)}}{\cot^{2}{\left(\frac{3 x}{2} \right)} + 1}$$

       /3*x\           /7*x\ 
  2*tan|---|      2*tan|---| 
       \ 2 /           \ 2 / 
------------- + -------------
       2/3*x\          2/7*x\
1 + tan |---|   1 + tan |---|
        \ 2 /           \ 2 /

$$\frac{2 \tan{\left(\frac{7 x}{2} \right)}}{\tan^{2}{\left(\frac{7 x}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{3 x}{2} \right)}}{\tan^{2}{\left(\frac{3 x}{2} \right)} + 1}$$

           2                          2            
------------------------ + ------------------------
/        1    \    /3*x\   /        1    \    /7*x\
|1 + ---------|*cot|---|   |1 + ---------|*cot|---|
|       2/3*x\|    \ 2 /   |       2/7*x\|    \ 2 /
|    cot |---||            |    cot |---||         
\        \ 2 //            \        \ 2 //

$$\frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{7 x}{2} \right)}}\right) \cot{\left(\frac{7 x}{2} \right)}} + \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{3 x}{2} \right)}}\right) \cot{\left(\frac{3 x}{2} \right)}}$$

//   0      for 3*x mod pi = 0\   //   0      for 7*x mod pi = 0\
|<                            | + |<                            |
\\sin(3*x)      otherwise     /   \\sin(7*x)      otherwise     /

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\sin{\left(3 x \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\sin{\left(7 x \right)} & \text{otherwise} \end{cases}\right)$$

        2/pi   3*x\           2/pi   7*x\
-1 + tan |-- + ---|   -1 + tan |-- + ---|
         \4     2 /            \4     2 /
------------------- + -------------------
        2/pi   3*x\           2/pi   7*x\
 1 + tan |-- + ---|    1 + tan |-- + ---|
         \4     2 /            \4     2 /

$$\frac{\tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{4} \right)} + 1} + \frac{\tan^{2}{\left(\frac{7 x}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{7 x}{2} + \frac{\pi}{4} \right)} + 1}$$

/       2/pi   3*x\\                  /       2/pi   7*x\\               
|1 - cot |-- + ---||*(1 + sin(3*x))   |1 - cot |-- + ---||*(1 + sin(7*x))
\        \4     2 //                  \        \4     2 //               
----------------------------------- + -----------------------------------
                 2                                     2

$$\frac{\left(- \cot^{2}{\left(\frac{3 x}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(3 x \right)} + 1\right)}{2} + \frac{\left(- \cot^{2}{\left(\frac{7 x}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(7 x \right)} + 1\right)}{2}$$

       2/pi   3*x\          2/pi   7*x\
1 - cot |-- + ---|   1 - cot |-- + ---|
        \4     2 /           \4     2 /
------------------ + ------------------
       2/pi   3*x\          2/pi   7*x\
1 + cot |-- + ---|   1 + cot |-- + ---|
        \4     2 /           \4     2 /

$$\frac{- \cot^{2}{\left(\frac{3 x}{2} + \frac{\pi}{4} \right)} + 1}{\cot^{2}{\left(\frac{3 x}{2} + \frac{\pi}{4} \right)} + 1} + \frac{- \cot^{2}{\left(\frac{7 x}{2} + \frac{\pi}{4} \right)} + 1}{\cot^{2}{\left(\frac{7 x}{2} + \frac{\pi}{4} \right)} + 1}$$

//   0      for 3*x mod pi = 0\   //   0      for 7*x mod pi = 0\
||                            |   ||                            |
|<   1                        | + |<   1                        |
||--------      otherwise     |   ||--------      otherwise     |
\\csc(3*x)                    /   \\csc(7*x)                    /

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\frac{1}{\csc{\left(3 x \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\frac{1}{\csc{\left(7 x \right)}} & \text{otherwise} \end{cases}\right)$$

//      0        for 3*x mod pi = 0\   //      0        for 7*x mod pi = 0\
||                                 |   ||                                 |
|<   /      pi\                    | + |<   /      pi\                    |
||cos|3*x - --|      otherwise     |   ||cos|7*x - --|      otherwise     |
\\   \      2 /                    /   \\   \      2 /                    /

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\cos{\left(3 x - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\cos{\left(7 x - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)$$

       2/3*x\                    2/7*x\          
  4*sin |---|*sin(3*x)      4*sin |---|*sin(7*x) 
        \ 2 /                     \ 2 /          
----------------------- + -----------------------
   2             4/3*x\      2             4/7*x\
sin (3*x) + 4*sin |---|   sin (7*x) + 4*sin |---|
                  \ 2 /                     \ 2 /

$$\frac{4 \sin^{2}{\left(\frac{7 x}{2} \right)} \sin{\left(7 x \right)}}{4 \sin^{4}{\left(\frac{7 x}{2} \right)} + \sin^{2}{\left(7 x \right)}} + \frac{4 \sin^{2}{\left(\frac{3 x}{2} \right)} \sin{\left(3 x \right)}}{4 \sin^{4}{\left(\frac{3 x}{2} \right)} + \sin^{2}{\left(3 x \right)}}$$

//      0        for 3*x mod pi = 0\   //      0        for 7*x mod pi = 0\
||                                 |   ||                                 |
||      1                          |   ||      1                          |
|<-------------      otherwise     | + |<-------------      otherwise     |
||   /      pi\                    |   ||   /      pi\                    |
||sec|3*x - --|                    |   ||sec|7*x - --|                    |
\\   \      2 /                    /   \\   \      2 /                    /

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\frac{1}{\sec{\left(3 x - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\frac{1}{\sec{\left(7 x - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)$$

//              /      3*pi\             \   //              /      3*pi\             \
||   1      for |3*x + ----| mod 2*pi = 0|   ||   1      for |7*x + ----| mod 2*pi = 0|
|<              \       2  /             | + |<              \       2  /             |
||                                       |   ||                                       |
\\sin(3*x)            otherwise          /   \\sin(7*x)            otherwise          /

$$\left(\begin{cases} 1 & \text{for}\: \left(3 x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(3 x \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: \left(7 x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(7 x \right)} & \text{otherwise} \end{cases}\right)$$

            2/3*x\                       2/7*x\        
       4*sin |---|                  4*sin |---|        
             \ 2 /                        \ 2 /        
-------------------------- + --------------------------
/         4/3*x\\            /         4/7*x\\         
|    4*sin |---||            |    4*sin |---||         
|          \ 2 /|            |          \ 2 /|         
|1 + -----------|*sin(3*x)   |1 + -----------|*sin(7*x)
|        2      |            |        2      |         
\     sin (3*x) /            \     sin (7*x) /

$$\frac{4 \sin^{2}{\left(\frac{7 x}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{7 x}{2} \right)}}{\sin^{2}{\left(7 x \right)}} + 1\right) \sin{\left(7 x \right)}} + \frac{4 \sin^{2}{\left(\frac{3 x}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{3 x}{2} \right)}}{\sin^{2}{\left(3 x \right)}} + 1\right) \sin{\left(3 x \right)}}$$

//     0        for 3*x mod pi = 0\   //     0        for 7*x mod pi = 0\
||                                |   ||                                |
||1 - cos(3*x)                    |   ||1 - cos(7*x)                    |
|<------------      otherwise     | + |<------------      otherwise     |
||     /3*x\                      |   ||     /7*x\                      |
||  tan|---|                      |   ||  tan|---|                      |
\\     \ 2 /                      /   \\     \ 2 /                      /

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\frac{- \cos{\left(3 x \right)} + 1}{\tan{\left(\frac{3 x}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\frac{- \cos{\left(7 x \right)} + 1}{\tan{\left(\frac{7 x}{2} \right)}} & \text{otherwise} \end{cases}\right)$$

//      0        for 3*x mod pi = 0\   //      0        for 7*x mod pi = 0\
||                                 |   ||                                 |
||       /3*x\                     |   ||       /7*x\                     |
||  2*tan|---|                     |   ||  2*tan|---|                     |
|<       \ 2 /                     | + |<       \ 2 /                     |
||-------------      otherwise     |   ||-------------      otherwise     |
||       2/3*x\                    |   ||       2/7*x\                    |
||1 + tan |---|                    |   ||1 + tan |---|                    |
\\        \ 2 /                    /   \\        \ 2 /                    /

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{3 x}{2} \right)}}{\tan^{2}{\left(\frac{3 x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{7 x}{2} \right)}}{\tan^{2}{\left(\frac{7 x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$

//      0        for 3*x mod pi = 0\   //      0        for 7*x mod pi = 0\
||                                 |   ||                                 |
||       /3*x\                     |   ||       /7*x\                     |
||  2*cot|---|                     |   ||  2*cot|---|                     |
|<       \ 2 /                     | + |<       \ 2 /                     |
||-------------      otherwise     |   ||-------------      otherwise     |
||       2/3*x\                    |   ||       2/7*x\                    |
||1 + cot |---|                    |   ||1 + cot |---|                    |
\\        \ 2 /                    /   \\        \ 2 /                    /

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{3 x}{2} \right)}}{\cot^{2}{\left(\frac{3 x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{7 x}{2} \right)}}{\cot^{2}{\left(\frac{7 x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$

//              0                for 3*x mod pi = 0\   //              0                for 7*x mod pi = 0\
||                                                 |   ||                                                 |
|

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\sin{\left(3 x \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\sin{\left(7 x \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$

//           0              for 3*x mod pi = 0\   //           0              for 7*x mod pi = 0\
||                                            |   ||                                            |
||           2                                |   ||           2                                |
||------------------------      otherwise     |   ||------------------------      otherwise     |
|

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{3 x}{2} \right)}}\right) \tan{\left(\frac{3 x}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{7 x}{2} \right)}}\right) \tan{\left(\frac{7 x}{2} \right)}} & \text{otherwise} \end{cases}\right)$$

            /  pi   3*x\                      /  pi   7*x\       
       2*cos|- -- + ---|                 2*cos|- -- + ---|       
            \  2     2 /                      \  2     2 /       
------------------------------- + -------------------------------
/       2/  pi   3*x\\            /       2/  pi   7*x\\         
|    cos |- -- + ---||            |    cos |- -- + ---||         
|        \  2     2 /|    /3*x\   |        \  2     2 /|    /7*x\
|1 + ----------------|*cos|---|   |1 + ----------------|*cos|---|
|          2/3*x\    |    \ 2 /   |          2/7*x\    |    \ 2 /
|       cos |---|    |            |       cos |---|    |         
\           \ 2 /    /            \           \ 2 /    /

$$\frac{2 \cos{\left(\frac{7 x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{7 x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{7 x}{2} \right)}}\right) \cos{\left(\frac{7 x}{2} \right)}} + \frac{2 \cos{\left(\frac{3 x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{3 x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{3 x}{2} \right)}}\right) \cos{\left(\frac{3 x}{2} \right)}}$$

                   /3*x\                                    /7*x\              
              2*sec|---|                               2*sec|---|              
                   \ 2 /                                    \ 2 /              
-------------------------------------- + --------------------------------------
/          2/3*x\    \                   /          2/7*x\    \                
|       sec |---|    |                   |       sec |---|    |                
|           \ 2 /    |    /  pi   3*x\   |           \ 2 /    |    /  pi   7*x\
|1 + ----------------|*sec|- -- + ---|   |1 + ----------------|*sec|- -- + ---|
|       2/  pi   3*x\|    \  2     2 /   |       2/  pi   7*x\|    \  2     2 /
|    sec |- -- + ---||                   |    sec |- -- + ---||                
\        \  2     2 //                   \        \  2     2 //

$$\frac{2 \sec{\left(\frac{7 x}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{7 x}{2} \right)}}{\sec^{2}{\left(\frac{7 x}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{7 x}{2} - \frac{\pi}{2} \right)}} + \frac{2 \sec{\left(\frac{3 x}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{3 x}{2} \right)}}{\sec^{2}{\left(\frac{3 x}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{3 x}{2} - \frac{\pi}{2} \right)}}$$

            /pi   3*x\                      /pi   7*x\       
       2*csc|-- - ---|                 2*csc|-- - ---|       
            \2     2 /                      \2     2 /       
----------------------------- + -----------------------------
/       2/pi   3*x\\            /       2/pi   7*x\\         
|    csc |-- - ---||            |    csc |-- - ---||         
|        \2     2 /|    /3*x\   |        \2     2 /|    /7*x\
|1 + --------------|*csc|---|   |1 + --------------|*csc|---|
|         2/3*x\   |    \ 2 /   |         2/7*x\   |    \ 2 /
|      csc |---|   |            |      csc |---|   |         
\          \ 2 /   /            \          \ 2 /   /

$$\frac{2 \csc{\left(- \frac{7 x}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{7 x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{7 x}{2} \right)}}\right) \csc{\left(\frac{7 x}{2} \right)}} + \frac{2 \csc{\left(- \frac{3 x}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{3 x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{3 x}{2} \right)}}\right) \csc{\left(\frac{3 x}{2} \right)}}$$

//               0                  for 3*x mod pi = 0\   //                0                  for 7*x mod pi = 0\
||                                                    |   ||                                                     |
||    -2*sin(6*x) + 4*sin(3*x)                        |   ||    -2*sin(14*x) + 4*sin(7*x)                        |
|<--------------------------------      otherwise     | + |<---------------------------------      otherwise     |
||                               2                    |   ||                                2                    |
||1 - cos(6*x) + 2*(1 - cos(3*x))                     |   ||1 - cos(14*x) + 2*(1 - cos(7*x))                     |
\\                                                    /   \\                                                     /

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\frac{4 \sin{\left(3 x \right)} - 2 \sin{\left(6 x \right)}}{2 \left(- \cos{\left(3 x \right)} + 1\right)^{2} - \cos{\left(6 x \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\frac{4 \sin{\left(7 x \right)} - 2 \sin{\left(14 x \right)}}{2 \left(- \cos{\left(7 x \right)} + 1\right)^{2} - \cos{\left(14 x \right)} + 1} & \text{otherwise} \end{cases}\right)$$

//                         /      3*pi\             \   //                         /      3*pi\             \
||         1           for |3*x + ----| mod 2*pi = 0|   ||         1           for |7*x + ----| mod 2*pi = 0|
||                         \       2  /             |   ||                         \       2  /             |
||                                                  |   ||                                                  |
||        2/pi   3*x\                               |   ||        2/pi   7*x\                               |
|<-1 + tan |-- + ---|                               | + |<-1 + tan |-- + ---|                               |
||         \4     2 /                               |   ||         \4     2 /                               |
||-------------------            otherwise          |   ||-------------------            otherwise          |
||        2/pi   3*x\                               |   ||        2/pi   7*x\                               |
|| 1 + tan |-- + ---|                               |   || 1 + tan |-- + ---|                               |
\\         \4     2 /                               /   \\         \4     2 /                               /

$$\left(\begin{cases} 1 & \text{for}\: \left(3 x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: \left(7 x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{7 x}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{7 x}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)$$

//             0               for 3*x mod pi = 0\   //             0               for 7*x mod pi = 0\
||                                               |   ||                                               |
||          sin(3*x)                             |   ||          sin(7*x)                             |
||---------------------------      otherwise     |   ||---------------------------      otherwise     |
||/        2      \                              |   ||/        2      \                              |
|<|     sin (3*x) |    2/3*x\                    | + |<|     sin (7*x) |    2/7*x\                    |
|||1 + -----------|*sin |---|                    |   |||1 + -----------|*sin |---|                    |
|||         4/3*x\|     \ 2 /                    |   |||         4/7*x\|     \ 2 /                    |
|||    4*sin |---||                              |   |||    4*sin |---||                              |
||\          \ 2 //                              |   ||\          \ 2 //                              |
\\                                               /   \\                                               /

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\frac{\sin{\left(3 x \right)}}{\left(1 + \frac{\sin^{2}{\left(3 x \right)}}{4 \sin^{4}{\left(\frac{3 x}{2} \right)}}\right) \sin^{2}{\left(\frac{3 x}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\frac{\sin{\left(7 x \right)}}{\left(1 + \frac{\sin^{2}{\left(7 x \right)}}{4 \sin^{4}{\left(\frac{7 x}{2} \right)}}\right) \sin^{2}{\left(\frac{7 x}{2} \right)}} & \text{otherwise} \end{cases}\right)$$

//                0                   for 3*x mod pi = 0\   //                0                   for 7*x mod pi = 0\
||                                                      |   ||                                                      |
||/      0        for 3*x mod pi = 0                    |   ||/      0        for 7*x mod pi = 0                    |
|||                                                     |   |||                                                     |
|||       /3*x\                                         |   |||       /7*x\                                         |
|<|  2*cot|---|                                         | + |<|  2*cot|---|                                         |
||<       \ 2 /                           otherwise     |   ||<       \ 2 /                           otherwise     |
|||-------------      otherwise                         |   |||-------------      otherwise                         |
|||       2/3*x\                                        |   |||       2/7*x\                                        |
|||1 + cot |---|                                        |   |||1 + cot |---|                                        |
\\\        \ 2 /                                        /   \\\        \ 2 /                                        /

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{3 x}{2} \right)}}{\cot^{2}{\left(\frac{3 x}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{7 x}{2} \right)}}{\cot^{2}{\left(\frac{7 x}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$

//                  0                     for 3*x mod pi = 0\   //                  0                     for 7*x mod pi = 0\
||                                                          |   ||                                                          |
||                   /3*x\                                  |   ||                   /7*x\                                  |
||              2*cos|---|                                  |   ||              2*cos|---|                                  |
||                   \ 2 /                                  |   ||                   \ 2 /                                  |
||--------------------------------------      otherwise     |   ||--------------------------------------      otherwise     |
|

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{3 x}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{3 x}{2} \right)}}{\cos^{2}{\left(\frac{3 x}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{3 x}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{7 x}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{7 x}{2} \right)}}{\cos^{2}{\left(\frac{7 x}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{7 x}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)$$

//               0                 for 3*x mod pi = 0\   //               0                 for 7*x mod pi = 0\
||                                                   |   ||                                                   |
||            /  pi   3*x\                           |   ||            /  pi   7*x\                           |
||       2*sec|- -- + ---|                           |   ||       2*sec|- -- + ---|                           |
||            \  2     2 /                           |   ||            \  2     2 /                           |
||-------------------------------      otherwise     |   ||-------------------------------      otherwise     |
|

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{3 x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{3 x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{3 x}{2} \right)}}\right) \sec{\left(\frac{3 x}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{7 x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{7 x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{7 x}{2} \right)}}\right) \sec{\left(\frac{7 x}{2} \right)}} & \text{otherwise} \end{cases}\right)$$

//                0                   for 3*x mod pi = 0\   //                0                   for 7*x mod pi = 0\
||                                                      |   ||                                                      |
||                 /3*x\                                |   ||                 /7*x\                                |
||            2*csc|---|                                |   ||            2*csc|---|                                |
||                 \ 2 /                                |   ||                 \ 2 /                                |
||----------------------------------      otherwise     |   ||----------------------------------      otherwise     |
|

$$\left(\begin{cases} 0 & \text{for}\: 3 x \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{3 x}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{3 x}{2} \right)}}{\csc^{2}{\left(- \frac{3 x}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{3 x}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 x \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{7 x}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{7 x}{2} \right)}}{\csc^{2}{\left(- \frac{7 x}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{7 x}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)$$

Piecewise((0, Mod(3*x = pi, 0)), (2*csc(3*x/2)/((1 + csc(3*x/2)^2/csc(pi/2 - 3*x/2)^2)*csc(pi/2 - 3*x/2)), True)) + Piecewise((0, Mod(7*x = pi, 0)), (2*csc(7*x/2)/((1 + csc(7*x/2)^2/csc(pi/2 - 7*x/2)^2)*csc(pi/2 - 7*x/2)), True))

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sin(7*x)+sin(3*x) если x=-1/3

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