Господин Экзамен

Lang:

Другие калькуляторы

Как пользоваться?
sqrt(4-4*sin(2*a))*sqrt(2-2*cos(2*a)) если a=-1/3
(7*p+2*q)^2+(7*p-2*q)^2 если q=-4
2*sin(6*x)*cos(6*x) если x=1/4
log(a*b)^2 если a=-1/3
Разложить многочлен на множители:
x^2-11*x+24
m^3+8
126*x^3+3*x^2+3*x+1
144-a^2
Общий знаменатель:
(u^2-2*u+4)/(4*u^2-1)*(2*u^2+4)/(u^3+8)
t/(t+3)^3-3/(t+3)^3
x^2-49/x^2+9*x*x^2-81/x^2-7*x
sqrt(2)/(sqrt(8)+2)-((6-sqrt(32))/sqrt(8)-3)
Умножение столбиком:
419*217
28*34
12*18
52*14
Деление столбиком:
1000/9
15/7
592/6
1219/3
Раскрыть скобки в:
(3*x-11)*2-5*(4-3*x)
7*(a+b)
26*(-a+b-c)
(a+2)*(a^2+2*a+4)
Разложение числа на простые множители:
31024
388
4860
6652
Производная:
1/4
Интеграл d{x}:
1/4
График функции y =:
1/4
Идентичные выражения
два *sin(шесть *x)*cos(шесть *x) если x= один / четыре
2 умножить на синус от (6 умножить на x) умножить на косинус от (6 умножить на x) если x равно 1 делить на 4
два умножить на синус от (шесть умножить на x) умножить на косинус от (шесть умножить на x) если x равно один делить на четыре
2sin(6x)cos(6x) если x=1/4
2sin6xcos6x если x=1/4
2*sin(6*x)*cos(6*x) при x=1/4
2*sin(6*x)*cos(6*x) если x=1 разделить на 4

Упрощение выражений/ 2*sin(6*x)*cos(6*x) если x=1/4

2sin(6x)cos(6x) если x=1/4

Решение

Вы ввели [src]

2*sin(6*x)*cos(6*x)

$$2 \sin{\left(6 x \right)} \cos{\left(6 x \right)}$$

2*sin(6*x)*cos(6*x)

Общее упрощение [src]

sin(12*x)

$$\sin{\left(12 x \right)}$$

sin(12*x)

Подстановка условия [src]

2*sin(6*x)*cos(6*x) при x = 1/4

подставляем

2*sin(6*x)*cos(6*x)

$$2 \sin{\left(6 x \right)} \cos{\left(6 x \right)}$$

sin(12*x)

$$\sin{\left(12 x \right)}$$

переменные

x = 1/4

$$x = \frac{1}{4}$$

sin(12*(1/4))

$$\sin{\left(12 (1/4) \right)}$$

sin(3)

$$\sin{\left(3 \right)}$$

sin(3)

Численный ответ [src]

2.0*cos(6*x)*sin(6*x)

2.0*cos(6*x)*sin(6*x)

Степени [src]

   / -6*I*x    6*I*x\                     
   |e         e     | /   -6*I*x    6*I*x\
-I*|------- + ------|*\- e       + e     /
   \   2        2   /

$$- i \left(\frac{e^{6 i x}}{2} + \frac{e^{- 6 i x}}{2}\right) \left(e^{6 i x} - e^{- 6 i x}\right)$$

-i*(exp(-6*i*x)/2 + exp(6*i*x)/2)*(-exp(-6*i*x) + exp(6*i*x))

Раскрыть выражение [src]

/        3       3            5                   5          \ /   6         6            4       2            2       4   \
\- 40*cos (x)*sin (x) + 12*cos (x)*sin(x) + 12*sin (x)*cos(x)/*\cos (x) - sin (x) - 15*cos (x)*sin (x) + 15*cos (x)*sin (x)/

$$\left(12 \sin^{5}{\left(x \right)} \cos{\left(x \right)} - 40 \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)} + 12 \sin{\left(x \right)} \cos^{5}{\left(x \right)}\right) \left(- \sin^{6}{\left(x \right)} + 15 \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)} - 15 \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)} + \cos^{6}{\left(x \right)}\right)$$

          5       5              7       3              3       3             5                   5                                      3                    3                    7                     3       5              7       5              5       3   
- 3072*cos (x)*sin (x) - 2048*cos (x)*sin (x) - 1152*cos (x)*sin (x) - 576*cos (x)*sin(x) - 64*sin (x)*cos(x) - 12*cos(x)*sin(x) + 64*sin (x)*cos(x) + 216*cos (x)*sin(x) + 384*cos (x)*sin(x) + 1152*cos (x)*sin (x) + 2048*cos (x)*sin (x) + 3072*cos (x)*sin (x)

$$2048 \sin^{5}{\left(x \right)} \cos^{7}{\left(x \right)} - 3072 \sin^{5}{\left(x \right)} \cos^{5}{\left(x \right)} - 2048 \sin^{3}{\left(x \right)} \cos^{7}{\left(x \right)} + 1152 \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)} + 3072 \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)} + 384 \sin{\left(x \right)} \cos^{7}{\left(x \right)} - 64 \sin^{5}{\left(x \right)} \cos{\left(x \right)} - 1152 \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)} - 576 \sin{\left(x \right)} \cos^{5}{\left(x \right)} + 64 \sin^{3}{\left(x \right)} \cos{\left(x \right)} + 216 \sin{\left(x \right)} \cos^{3}{\left(x \right)} - 12 \sin{\left(x \right)} \cos{\left(x \right)}$$

-3072*cos(x)^5*sin(x)^5 - 2048*cos(x)^7*sin(x)^3 - 1152*cos(x)^3*sin(x)^3 - 576*cos(x)^5*sin(x) - 64*sin(x)^5*cos(x) - 12*cos(x)*sin(x) + 64*sin(x)^3*cos(x) + 216*cos(x)^3*sin(x) + 384*cos(x)^7*sin(x) + 1152*cos(x)^3*sin(x)^5 + 2048*cos(x)^7*sin(x)^5 + 3072*cos(x)^5*sin(x)^3

Собрать выражение [src]

sin(12*x)

$$\sin{\left(12 x \right)}$$

sin(12*x)

Тригонометрическая часть [src]

sin(12*x)

$$\sin{\left(12 x \right)}$$

    1    
---------
csc(12*x)

$$\frac{1}{\csc{\left(12 x \right)}}$$

   /       pi\
cos|12*x - --|
   \       2 /

$$\cos{\left(12 x - \frac{\pi}{2} \right)}$$

      1       
--------------
   /       pi\
sec|12*x - --|
   \       2 /

$$\frac{1}{\sec{\left(12 x - \frac{\pi}{2} \right)}}$$

        2        
-----------------
csc(6*x)*sec(6*x)

$$\frac{2}{\csc{\left(6 x \right)} \sec{\left(6 x \right)}}$$

  2*tan(6*x) 
-------------
       2     
1 + tan (6*x)

$$\frac{2 \tan{\left(6 x \right)}}{\tan^{2}{\left(6 x \right)} + 1}$$

              /pi      \
2*sin(6*x)*sin|-- + 6*x|
              \2       /

$$2 \sin{\left(6 x \right)} \sin{\left(6 x + \frac{\pi}{2} \right)}$$

              /      pi\
2*cos(6*x)*cos|6*x - --|
              \      2 /

$$2 \cos{\left(6 x \right)} \cos{\left(6 x - \frac{\pi}{2} \right)}$$

          2           
----------------------
            /      pi\
sec(6*x)*sec|6*x - --|
            \      2 /

$$\frac{2}{\sec{\left(6 x \right)} \sec{\left(6 x - \frac{\pi}{2} \right)}}$$

          2           
----------------------
            /pi      \
sec(6*x)*sec|-- - 6*x|
            \2       /

$$\frac{2}{\sec{\left(6 x \right)} \sec{\left(- 6 x + \frac{\pi}{2} \right)}}$$

          2           
----------------------
            /pi      \
csc(6*x)*csc|-- - 6*x|
            \2       /

$$\frac{2}{\csc{\left(6 x \right)} \csc{\left(- 6 x + \frac{\pi}{2} \right)}}$$

  /          2     \         
2*\-1 + 2*cos (3*x)/*sin(6*x)

$$2 \cdot \left(2 \cos^{2}{\left(3 x \right)} - 1\right) \sin{\left(6 x \right)}$$

             2             
---------------------------
                 /pi      \
csc(pi - 6*x)*csc|-- - 6*x|
                 \2       /

$$\frac{2}{\csc{\left(- 6 x + \pi \right)} \csc{\left(- 6 x + \frac{\pi}{2} \right)}}$$

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

$$4 \cdot \left(2 \cos^{2}{\left(3 x \right)} - 1\right) \sin{\left(3 x \right)} \cos{\left(3 x \right)}$$

/    0      for 12*x mod pi = 0
<                              
\sin(12*x)       otherwise

$$\begin{cases} 0 & \text{for}\: 12 x \bmod \pi = 0 \\\sin{\left(12 x \right)} & \text{otherwise} \end{cases}$$

  /   2           2     \                  
4*\cos (3*x) - sin (3*x)/*cos(3*x)*sin(3*x)

$$4 \left(- \sin^{2}{\left(3 x \right)} + \cos^{2}{\left(3 x \right)}\right) \sin{\left(3 x \right)} \cos{\left(3 x \right)}$$

  /       2     \         
4*\1 - tan (3*x)/*tan(3*x)
--------------------------
                    2     
     /       2     \      
     \1 + tan (3*x)/

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

/      0        for 12*x mod pi = 0
|                                  
|  2*cot(6*x)                      
<-------------       otherwise     
|       2                          
|1 + cot (6*x)                     
\

$$\begin{cases} 0 & \text{for}\: 12 x \bmod \pi = 0 \\\frac{2 \cot{\left(6 x \right)}}{\cot^{2}{\left(6 x \right)} + 1} & \text{otherwise} \end{cases}$$

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

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

   2      /       2/      pi\\ /       2     \               
cos (3*x)*|1 - cot |3*x + --||*\1 - tan (3*x)/*(1 + sin(6*x))
          \        \      4 //

$$\left(- \tan^{2}{\left(3 x \right)} + 1\right) \left(- \cot^{2}{\left(3 x + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(6 x \right)} + 1\right) \cos^{2}{\left(3 x \right)}$$

                    /      pi\      
      8*tan(3*x)*tan|3*x + --|      
                    \      4 /      
------------------------------------
/       2     \ /       2/      pi\\
\1 + tan (3*x)/*|1 + tan |3*x + --||
                \        \      4 //

$$\frac{8 \tan{\left(3 x \right)} \tan{\left(3 x + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(3 x \right)} + 1\right) \left(\tan^{2}{\left(3 x + \frac{\pi}{4} \right)} + 1\right)}$$

                    /      pi\      
      8*cot(3*x)*tan|3*x + --|      
                    \      4 /      
------------------------------------
/       2     \ /       2/      pi\\
\1 + cot (3*x)/*|1 + tan |3*x + --||
                \        \      4 //

$$\frac{8 \tan{\left(3 x + \frac{\pi}{4} \right)} \cot{\left(3 x \right)}}{\left(\tan^{2}{\left(3 x + \frac{\pi}{4} \right)} + 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right)}$$

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

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

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

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

            /         4     \
     2      |    4*sin (3*x)|
8*sin (3*x)*|1 - -----------|
            |        2      |
            \     sin (6*x) /
-----------------------------
                  2          
 /         4     \           
 |    4*sin (3*x)|           
 |1 + -----------| *sin(6*x) 
 |        2      |           
 \     sin (6*x) /

$$\frac{8 \left(- \frac{4 \sin^{4}{\left(3 x \right)}}{\sin^{2}{\left(6 x \right)}} + 1\right) \sin^{2}{\left(3 x \right)}}{\left(\frac{4 \sin^{4}{\left(3 x \right)}}{\sin^{2}{\left(6 x \right)}} + 1\right)^{2} \sin{\left(6 x \right)}}$$

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

$$2 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\sin{\left(6 x \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: 3 x \bmod \pi = 0 \\\cos{\left(6 x \right)} & \text{otherwise} \end{cases}\right)$$

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

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

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

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

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

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

    /         2        \           
    |      sec (3*x)   |           
  4*|1 - --------------|*sec(3*x)  
    |       2/      pi\|           
    |    sec |3*x - --||           
    \        \      2 //           
-----------------------------------
                    2              
/         2        \               
|      sec (3*x)   |     /      pi\
|1 + --------------| *sec|3*x - --|
|       2/      pi\|     \      2 /
|    sec |3*x - --||               
\        \      2 //

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

  //      0        for 6*x mod pi = 0\                                
  ||                                 | //   1      for 3*x mod pi = 0\
  ||      1                          | ||                            |
2*|<-------------      otherwise     |*|<   1                        |
  ||   /      pi\                    | ||--------      otherwise     |
  ||sec|6*x - --|                    | \\sec(6*x)                    /
  \\   \      2 /                    /

$$2 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\frac{1}{\sec{\left(6 x - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: 3 x \bmod \pi = 0 \\\frac{1}{\sec{\left(6 x \right)}} & \text{otherwise} \end{cases}\right)$$

                                  //      1        for 3*x mod pi = 0\
  //   0      for 6*x mod pi = 0\ ||                                 |
  ||                            | ||      1                          |
2*|<   1                        |*|<-------------      otherwise     |
  ||--------      otherwise     | ||   /pi      \                    |
  \\csc(6*x)                    / ||csc|-- - 6*x|                    |
                                  \\   \2       /                    /

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

  /       2/      pi\\              
  |    cos |3*x - --||              
  |        \      2 /|    /      pi\
4*|1 - --------------|*cos|3*x - --|
  |         2        |    \      2 /
  \      cos (3*x)   /              
------------------------------------
                       2            
   /       2/      pi\\             
   |    cos |3*x - --||             
   |        \      2 /|             
   |1 + --------------| *cos(3*x)   
   |         2        |             
   \      cos (3*x)   /

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

  /       2/pi      \\              
  |    csc |-- - 3*x||              
  |        \2       /|    /pi      \
4*|1 - --------------|*csc|-- - 3*x|
  |         2        |    \2       /
  \      csc (3*x)   /              
------------------------------------
                       2            
   /       2/pi      \\             
   |    csc |-- - 3*x||             
   |        \2       /|             
   |1 + --------------| *csc(3*x)   
   |         2        |             
   \      csc (3*x)   /

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

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

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

  //      0        for 6*x mod pi = 0\ //      1         for 3*x mod pi = 0\
  ||                                 | ||                                  |
  ||  2*cot(3*x)                     | ||        2                         |
2*|<-------------      otherwise     |*|<-1 + cot (3*x)                    |
  ||       2                         | ||--------------      otherwise     |
  ||1 + cot (3*x)                    | ||       2                          |
  \\                                 / \\1 + cot (3*x)                     /

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

  //      0        for 6*x mod pi = 0\ //      1        for 3*x mod pi = 0\
  ||                                 | ||                                 |
  ||  2*tan(3*x)                     | ||       2                         |
2*|<-------------      otherwise     |*|<1 - tan (3*x)                    |
  ||       2                         | ||-------------      otherwise     |
  ||1 + tan (3*x)                    | ||       2                         |
  \\                                 / \\1 + tan (3*x)                    /

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

                                                  //      1         for 3*x mod pi = 0\
  //           0              for 6*x mod pi = 0\ ||                                  |
  ||                                            | ||         1                        |
  ||           2                                | ||-1 + ---------                    |
  ||------------------------      otherwise     | ||        2                         |
2*|

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

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

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

                                        //                         /      3*pi\             \
                                        ||         1           for |6*x + ----| mod 2*pi = 0|
  //      1         for 3*x mod pi = 0\ ||                         \       2  /             |
  ||                                  | ||                                                  |
  ||        2                         | ||        2/      pi\                               |
2*|<-1 + cot (3*x)                    |*|<-1 + tan |3*x + --|                               |
  ||--------------      otherwise     | ||         \      4 /                               |
  ||       2                          | ||-------------------            otherwise          |
  \\1 + cot (3*x)                     / ||        2/      pi\                               |
                                        || 1 + tan |3*x + --|                               |
                                        \\         \      4 /                               /

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

  //              0                for 6*x mod pi = 0\ //              1                for 3*x mod pi = 0\
  ||                                                 | ||                                                 |
2*|

$$2 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\sin{\left(6 x \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: 3 x \bmod \pi = 0 \\\begin{cases} 1 & \text{for}\: 3 x \bmod \pi = 0 \\\cos{\left(6 x \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$

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

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

  //                0                   for 6*x mod pi = 0\ //                 1                   for 3*x mod pi = 0\
  ||                                                      | ||                                                       |
  ||/      0        for 6*x mod pi = 0                    | ||/      1         for 3*x mod pi = 0                    |
  |||                                                     | |||                                                      |
2*|<|  2*cot(3*x)                                         |*|<|        2                                             |
  ||<-------------      otherwise           otherwise     | ||<-1 + cot (3*x)                          otherwise     |
  |||       2                                             | |||--------------      otherwise                         |
  |||1 + cot (3*x)                                        | |||       2                                              |
  \\\                                                     / \\\1 + cot (3*x)                                         /

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

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

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

                                                       //         1           for 3*x mod pi = 0\
  //              0                for 6*x mod pi = 0\ ||                                       |
  ||                                                 | ||        2/      pi\                    |
  ||            /      pi\                           | ||     sec |3*x - --|                    |
  ||       2*sec|3*x - --|                           | ||         \      2 /                    |
  ||            \      2 /                           | ||-1 + --------------                    |
  ||-----------------------------      otherwise     | ||          2                            |
2*|

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

                                                            //         1           for 3*x mod pi = 0\
                                                            ||                                       |
  //                0                   for 6*x mod pi = 0\ ||          2                            |
  ||                                                      | ||       csc (3*x)                       |
  ||            2*csc(3*x)                                | ||-1 + --------------                    |
  ||----------------------------------      otherwise     | ||        2/pi      \                    |
  ||/         2        \                                  | ||     csc |-- - 3*x|                    |
2*|<|      csc (3*x)   |    /pi      \                    |*|<         \2       /                    |
  |||1 + --------------|*csc|-- - 3*x|                    | ||-------------------      otherwise     |
  |||       2/pi      \|    \2       /                    | ||          2                            |
  |||    csc |-- - 3*x||                                  | ||       csc (3*x)                       |
  ||\        \2       //                                  | || 1 + --------------                    |
  \\                                                      / ||        2/pi      \                    |
                                                            ||     csc |-- - 3*x|                    |
                                                            \\         \2       /                    /

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

2*Piecewise((0, Mod(6*x = pi, 0)), (2*csc(3*x)/((1 + csc(3*x)^2/csc(pi/2 - 3*x)^2)*csc(pi/2 - 3*x)), True))*Piecewise((1, Mod(3*x = pi, 0)), ((-1 + csc(3*x)^2/csc(pi/2 - 3*x)^2)/(1 + csc(3*x)^2/csc(pi/2 - 3*x)^2), True))

Другие калькуляторы

Как пользоваться?

Идентичные выражения

2*sin(6*x)*cos(6*x) если x=1/4

Решение

2sin(6x)cos(6x) если x=1/4