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Simplificación de expresiones/ Descomposición en fracciones simples/ cos(x)/(1-sin(2*x))+2*cos(2*x)*sin(x)/(1-sin(2*x))^2

¿Cómo vas a descomponer esta cos(x)/(1-sin(2*x))+2*cos(2*x)*sin(x)/(1-sin(2*x))^2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   cos(x)      2*cos(2*x)*sin(x)
------------ + -----------------
1 - sin(2*x)                  2 
                (1 - sin(2*x))
sin⁡(x)2cos⁡(2x)(1−sin⁡(2x))2+cos⁡(x)1−sin⁡(2x)\frac{\sin{\left(x \right)} 2 \cos{\left(2 x \right)}}{\left(1 - \sin{\left(2 x \right)}\right)^{2}} + \frac{\cos{\left(x \right)}}{1 - \sin{\left(2 x \right)}} 
cos(x)/(1 - sin(2*x)) + ((2*cos(2*x))*sin(x))/(1 - sin(2*x))^2
Simplificación general [src] 
       3            
- 2*sin (x) + cos(x)
--------------------
                 2  
  (-1 + sin(2*x))
−2sin⁡3(x)+cos⁡(x)(sin⁡(2x)−1)2\frac{- 2 \sin^{3}{\left(x \right)} + \cos{\left(x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} 
(-2*sin(x)^3 + cos(x))/(-1 + sin(2*x))^2
Denominador racional [src] 
              2                                          
(1 - sin(2*x)) *cos(x) + 2*(1 - sin(2*x))*cos(2*x)*sin(x)
---------------------------------------------------------
                                   3                     
                     (1 - sin(2*x))
(1−sin⁡(2x))2cos⁡(x)+2(1−sin⁡(2x))sin⁡(x)cos⁡(2x)(1−sin⁡(2x))3\frac{\left(1 - \sin{\left(2 x \right)}\right)^{2} \cos{\left(x \right)} + 2 \left(1 - \sin{\left(2 x \right)}\right) \sin{\left(x \right)} \cos{\left(2 x \right)}}{\left(1 - \sin{\left(2 x \right)}\right)^{3}} 
((1 - sin(2*x))^2*cos(x) + 2*(1 - sin(2*x))*cos(2*x)*sin(x))/(1 - sin(2*x))^3
Combinatoria [src] 
-cos(x)*sin(2*x) + 2*cos(2*x)*sin(x) + cos(x)
---------------------------------------------
                              2              
               (-1 + sin(2*x))
2sin⁡(x)cos⁡(2x)−sin⁡(2x)cos⁡(x)+cos⁡(x)(sin⁡(2x)−1)2\frac{2 \sin{\left(x \right)} \cos{\left(2 x \right)} - \sin{\left(2 x \right)} \cos{\left(x \right)} + \cos{\left(x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} 
(-cos(x)*sin(2*x) + 2*cos(2*x)*sin(x) + cos(x))/(-1 + sin(2*x))^2
Denominador común [src] 
-cos(x)*sin(2*x) + 2*cos(2*x)*sin(x) + cos(x)
---------------------------------------------
                 2                           
          1 + sin (2*x) - 2*sin(2*x)
2sin⁡(x)cos⁡(2x)−sin⁡(2x)cos⁡(x)+cos⁡(x)sin⁡2(2x)−2sin⁡(2x)+1\frac{2 \sin{\left(x \right)} \cos{\left(2 x \right)} - \sin{\left(2 x \right)} \cos{\left(x \right)} + \cos{\left(x \right)}}{\sin^{2}{\left(2 x \right)} - 2 \sin{\left(2 x \right)} + 1} 
(-cos(x)*sin(2*x) + 2*cos(2*x)*sin(x) + cos(x))/(1 + sin(2*x)^2 - 2*sin(2*x))
Unión de expresiones racionales [src] 
(1 - sin(2*x))*cos(x) + 2*cos(2*x)*sin(x)
-----------------------------------------
                           2             
             (1 - sin(2*x))
(1−sin⁡(2x))cos⁡(x)+2sin⁡(x)cos⁡(2x)(1−sin⁡(2x))2\frac{\left(1 - \sin{\left(2 x \right)}\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(2 x \right)}}{\left(1 - \sin{\left(2 x \right)}\right)^{2}} 
((1 - sin(2*x))*cos(x) + 2*cos(2*x)*sin(x))/(1 - sin(2*x))^2
Potencias [src] 
        I*x    -I*x                                               
       e      e                                                   
       ---- + -----            /   -I*x    I*x\ / -2*I*x    2*I*x\
        2       2            I*\- e     + e   /*\e       + e     /
-------------------------- - -------------------------------------
      /   -2*I*x    2*I*x\                                    2   
    I*\- e       + e     /        /      /   -2*I*x    2*I*x\\    
1 + ----------------------        |    I*\- e       + e     /|    
              2                 2*|1 + ----------------------|    
                                  \              2           /
eix2+e−ix2i(e2ix−e−2ix)2+1−i(eix−e−ix)(e2ix+e−2ix)2(i(e2ix−e−2ix)2+1)2\frac{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}{\frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2} + 1} - \frac{i \left(e^{i x} - e^{- i x}\right) \left(e^{2 i x} + e^{- 2 i x}\right)}{2 \left(\frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2} + 1\right)^{2}} 
   cos(x)      2*cos(2*x)*sin(x)
------------ + -----------------
1 - sin(2*x)                  2 
                (1 - sin(2*x))
cos⁡(x)1−sin⁡(2x)+2sin⁡(x)cos⁡(2x)(1−sin⁡(2x))2\frac{\cos{\left(x \right)}}{1 - \sin{\left(2 x \right)}} + \frac{2 \sin{\left(x \right)} \cos{\left(2 x \right)}}{\left(1 - \sin{\left(2 x \right)}\right)^{2}} 
cos(x)/(1 - sin(2*x)) + 2*cos(2*x)*sin(x)/(1 - sin(2*x))^2
Compilar la expresión [src] 
   cos(x)      2*cos(2*x)*sin(x)
------------ + -----------------
1 - sin(2*x)                  2 
                (1 - sin(2*x))
cos⁡(x)1−sin⁡(2x)+2sin⁡(x)cos⁡(2x)(1−sin⁡(2x))2\frac{\cos{\left(x \right)}}{1 - \sin{\left(2 x \right)}} + \frac{2 \sin{\left(x \right)} \cos{\left(2 x \right)}}{\left(1 - \sin{\left(2 x \right)}\right)^{2}} 
cos(x)/(1 - sin(2*x)) + 2*cos(2*x)*sin(x)/(1 - sin(2*x))^2
Abrimos la expresión [src] 
                                                                                 2                     
       cos(x)                         2*sin(x)                              4*cos (x)*sin(x)           
------------------- - --------------------------------------- + ---------------------------------------
1 - 2*cos(x)*sin(x)                              2       2                                 2       2   
                      1 - 4*cos(x)*sin(x) + 4*cos (x)*sin (x)   1 - 4*cos(x)*sin(x) + 4*cos (x)*sin (x)
4sin⁡(x)cos⁡2(x)4sin⁡2(x)cos⁡2(x)−4sin⁡(x)cos⁡(x)+1−2sin⁡(x)4sin⁡2(x)cos⁡2(x)−4sin⁡(x)cos⁡(x)+1+cos⁡(x)−2sin⁡(x)cos⁡(x)+1\frac{4 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{4 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} - 4 \sin{\left(x \right)} \cos{\left(x \right)} + 1} - \frac{2 \sin{\left(x \right)}}{4 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} - 4 \sin{\left(x \right)} \cos{\left(x \right)} + 1} + \frac{\cos{\left(x \right)}}{- 2 \sin{\left(x \right)} \cos{\left(x \right)} + 1} 
cos(x)/(1 - 2*cos(x)*sin(x)) - 2*sin(x)/(1 - 4*cos(x)*sin(x) + 4*cos(x)^2*sin(x)^2) + 4*cos(x)^2*sin(x)/(1 - 4*cos(x)*sin(x) + 4*cos(x)^2*sin(x)^2)
Parte trigonométrica [src] 
            1                                    2                    
-------------------------- + -----------------------------------------
/          1      \                             2                     
|1 - -------------|*sec(x)   /          1      \              /    pi\
|       /      pi\|          |1 - -------------| *sec(2*x)*sec|x - --|
|    sec|2*x - --||          |       /      pi\|              \    2 /
\       \      2 //          |    sec|2*x - --||                      
                             \       \      2 //
1(1−1sec⁡(2x−π2))sec⁡(x)+2(1−1sec⁡(2x−π2))2sec⁡(2x)sec⁡(x−π2)\frac{1}{\left(1 - \frac{1}{\sec{\left(2 x - \frac{\pi}{2} \right)}}\right) \sec{\left(x \right)}} + \frac{2}{\left(1 - \frac{1}{\sec{\left(2 x - \frac{\pi}{2} \right)}}\right)^{2} \sec{\left(2 x \right)} \sec{\left(x - \frac{\pi}{2} \right)}} 
        3/    pi\           
 - 2*cos |x - --| + cos(x)  
         \    2 /           
----------------------------
                           2
/                 /    pi\\ 
|-1 + 2*cos(x)*cos|x - --|| 
\                 \    2 //
cos⁡(x)−2cos⁡3(x−π2)(2cos⁡(x)cos⁡(x−π2)−1)2\frac{\cos{\left(x \right)} - 2 \cos^{3}{\left(x - \frac{\pi}{2} \right)}}{\left(2 \cos{\left(x \right)} \cos{\left(x - \frac{\pi}{2} \right)} - 1\right)^{2}} 
                  2/x\                         /        2   \    /x\            
          -1 + cot |-|                       4*\-1 + cot (x)/*cot|-|            
                   \2/                                           \2/            
------------------------------- + ----------------------------------------------
/       2/x\\ /      2*cot(x) \                                                2
|1 + cot |-||*|1 - -----------|   /       2   \ /       2/x\\ /      2*cot(x) \ 
\        \2// |           2   |   \1 + cot (x)/*|1 + cot |-||*|1 - -----------| 
              \    1 + cot (x)/                 \        \2// |           2   | 
                                                              \    1 + cot (x)/
cot⁡2(x2)−1(1−2cot⁡(x)cot⁡2(x)+1)(cot⁡2(x2)+1)+4(cot⁡2(x)−1)cot⁡(x2)(1−2cot⁡(x)cot⁡2(x)+1)2(cot⁡2(x2)+1)(cot⁡2(x)+1)\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\left(1 - \frac{2 \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{4 \left(\cot^{2}{\left(x \right)} - 1\right) \cot{\left(\frac{x}{2} \right)}}{\left(1 - \frac{2 \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1}\right)^{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)} 
        2/x\           3/x\   
 1 - tan |-|     16*tan |-|   
         \2/            \2/   
 ----------- - -------------- 
        2/x\                3 
 1 + tan |-|   /       2/x\\  
         \2/   |1 + tan |-||  
               \        \2//  
------------------------------
                             2
/       /       2/x\\    /x\\ 
|     4*|1 - tan |-||*tan|-|| 
|       \        \2//    \2/| 
|-1 + ----------------------| 
|                      2    | 
|         /       2/x\\     | 
|         |1 + tan |-||     | 
\         \        \2//     /
1−tan⁡2(x2)tan⁡2(x2)+1−16tan⁡3(x2)(tan⁡2(x2)+1)3(4(1−tan⁡2(x2))tan⁡(x2)(tan⁡2(x2)+1)2−1)2\frac{\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{16 \tan^{3}{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{3}}}{\left(\frac{4 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \tan{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} - 1\right)^{2}} 
        3         /    pi\  
 - 2*sin (x) + sin|x + --|  
                  \    2 /  
----------------------------
                           2
/                 /    pi\\ 
|-1 + 2*sin(x)*sin|x + --|| 
\                 \    2 //
−2sin⁡3(x)+sin⁡(x+π2)(2sin⁡(x)sin⁡(x+π2)−1)2\frac{- 2 \sin^{3}{\left(x \right)} + \sin{\left(x + \frac{\pi}{2} \right)}}{\left(2 \sin{\left(x \right)} \sin{\left(x + \frac{\pi}{2} \right)} - 1\right)^{2}} 
   /      pi\        /    pi\         
cos|3*x - --|   3*cos|x - --|         
   \      2 /        \    2 /         
------------- - ------------- + cos(x)
      2               2               
--------------------------------------
                            2         
        /        /      pi\\          
        |-1 + cos|2*x - --||          
        \        \      2 //
cos⁡(x)−3cos⁡(x−π2)2+cos⁡(3x−π2)2(cos⁡(2x−π2)−1)2\frac{\cos{\left(x \right)} - \frac{3 \cos{\left(x - \frac{\pi}{2} \right)}}{2} + \frac{\cos{\left(3 x - \frac{\pi}{2} \right)}}{2}}{\left(\cos{\left(2 x - \frac{\pi}{2} \right)} - 1\right)^{2}} 
            1                                 2                  
-------------------------- + ------------------------------------
/       1    \    /pi    \                 2                     
|1 - --------|*csc|-- - x|   /       1    \            /pi      \
\    csc(2*x)/    \2     /   |1 - --------| *csc(x)*csc|-- - 2*x|
                             \    csc(2*x)/            \2       /
1(1−1csc⁡(2x))csc⁡(−x+π2)+2(1−1csc⁡(2x))2csc⁡(x)csc⁡(−2x+π2)\frac{1}{\left(1 - \frac{1}{\csc{\left(2 x \right)}}\right) \csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{2}{\left(1 - \frac{1}{\csc{\left(2 x \right)}}\right)^{2} \csc{\left(x \right)} \csc{\left(- 2 x + \frac{\pi}{2} \right)}} 
       2/x\         /3*x\            /x\ 
1 - tan |-|      tan|---|       3*tan|-| 
        \2/         \ 2 /            \2/ 
----------- + ------------- - -----------
       2/x\          2/3*x\          2/x\
1 + tan |-|   1 + tan |---|   1 + tan |-|
        \2/           \ 2 /           \2/
-----------------------------------------
                             2           
           /       2*tan(x) \            
           |-1 + -----------|            
           |            2   |            
           \     1 + tan (x)/
1−tan⁡2(x2)tan⁡2(x2)+1+tan⁡(3x2)tan⁡2(3x2)+1−3tan⁡(x2)tan⁡2(x2)+1(−1+2tan⁡(x)tan⁡2(x)+1)2\frac{\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\tan{\left(\frac{3 x}{2} \right)}}{\tan^{2}{\left(\frac{3 x}{2} \right)} + 1} - \frac{3 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}}{\left(-1 + \frac{2 \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\right)^{2}} 
                 2/x\                           /       2   \    /x\            
          1 - tan |-|                         4*\1 - tan (x)/*tan|-|            
                  \2/                                            \2/            
------------------------------- + ----------------------------------------------
/       2/x\\ /      2*tan(x) \                                                2
|1 + tan |-||*|1 - -----------|   /       2   \ /       2/x\\ /      2*tan(x) \ 
\        \2// |           2   |   \1 + tan (x)/*|1 + tan |-||*|1 - -----------| 
              \    1 + tan (x)/                 \        \2// |           2   | 
                                                              \    1 + tan (x)/
1−tan⁡2(x2)(1−2tan⁡(x)tan⁡2(x)+1)(tan⁡2(x2)+1)+4(1−tan⁡2(x))tan⁡(x2)(1−2tan⁡(x)tan⁡2(x)+1)2(tan⁡2(x2)+1)(tan⁡2(x)+1)\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\left(1 - \frac{2 \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{4 \left(1 - \tan^{2}{\left(x \right)}\right) \tan{\left(\frac{x}{2} \right)}}{\left(1 - \frac{2 \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\right)^{2} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)} 
sin(3*x)   3*sin(x)         
-------- - -------- + cos(x)
   2          2             
----------------------------
                     2      
      (-1 + sin(2*x))
−3sin⁡(x)2+sin⁡(3x)2+cos⁡(x)(sin⁡(2x)−1)2\frac{- \frac{3 \sin{\left(x \right)}}{2} + \frac{\sin{\left(3 x \right)}}{2} + \cos{\left(x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} 
         2/x\           3/x\   
 -1 + cot |-|     16*cot |-|   
          \2/            \2/   
 ------------ - -------------- 
        2/x\                 3 
 1 + cot |-|    /       2/x\\  
         \2/    |1 + cot |-||  
                \        \2//  
-------------------------------
                              2
/       /        2/x\\    /x\\ 
|     4*|-1 + cot |-||*cot|-|| 
|       \         \2//    \2/| 
|-1 + -----------------------| 
|                       2    | 
|          /       2/x\\     | 
|          |1 + cot |-||     | 
\          \        \2//     /
cot⁡2(x2)−1cot⁡2(x2)+1−16cot⁡3(x2)(cot⁡2(x2)+1)3(4(cot⁡2(x2)−1)cot⁡(x2)(cot⁡2(x2)+1)2−1)2\frac{\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{16 \cot^{3}{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{3}}}{\left(\frac{4 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \cot{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} - 1\right)^{2}} 
  1             1                3      
------ + --------------- - -------------
sec(x)        /      pi\        /    pi\
         2*sec|3*x - --|   2*sec|x - --|
              \      2 /        \    2 /
----------------------------------------
                             2          
         /           1      \           
         |-1 + -------------|           
         |        /      pi\|           
         |     sec|2*x - --||           
         \        \      2 //
12sec⁡(3x−π2)−32sec⁡(x−π2)+1sec⁡(x)(−1+1sec⁡(2x−π2))2\frac{\frac{1}{2 \sec{\left(3 x - \frac{\pi}{2} \right)}} - \frac{3}{2 \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(x \right)}}}{\left(-1 + \frac{1}{\sec{\left(2 x - \frac{\pi}{2} \right)}}\right)^{2}} 
    1           2         
  ------ - ------------   
  sec(x)      3/    pi\   
           sec |x - --|   
               \    2 /   
--------------------------
                         2
/             2         \ 
|-1 + ------------------| 
|               /    pi\| 
|     sec(x)*sec|x - --|| 
\               \    2 //
−2sec⁡3(x−π2)+1sec⁡(x)(−1+2sec⁡(x)sec⁡(x−π2))2\frac{- \frac{2}{\sec^{3}{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(x \right)}}}{\left(-1 + \frac{2}{\sec{\left(x \right)} \sec{\left(x - \frac{\pi}{2} \right)}}\right)^{2}} 
   cos(x)      2*cos(2*x)*sin(x)
------------ + -----------------
1 - sin(2*x)                  2 
                (1 - sin(2*x))
cos⁡(x)1−sin⁡(2x)+2sin⁡(x)cos⁡(2x)(1−sin⁡(2x))2\frac{\cos{\left(x \right)}}{1 - \sin{\left(2 x \right)}} + \frac{2 \sin{\left(x \right)} \cos{\left(2 x \right)}}{\left(1 - \sin{\left(2 x \right)}\right)^{2}} 
   /    pi\                /pi      \
sin|x + --|    2*sin(x)*sin|-- + 2*x|
   \    2 /                \2       /
------------ + ----------------------
1 - sin(2*x)                    2    
                  (1 - sin(2*x))
sin⁡(x+π2)1−sin⁡(2x)+2sin⁡(x)sin⁡(2x+π2)(1−sin⁡(2x))2\frac{\sin{\left(x + \frac{\pi}{2} \right)}}{1 - \sin{\left(2 x \right)}} + \frac{2 \sin{\left(x \right)} \sin{\left(2 x + \frac{\pi}{2} \right)}}{\left(1 - \sin{\left(2 x \right)}\right)^{2}} 
       1           2      
  ----------- - -------   
     /pi    \      3      
  csc|-- - x|   csc (x)   
     \2     /             
--------------------------
                         2
/             2         \ 
|-1 + ------------------| 
|               /pi    \| 
|     csc(x)*csc|-- - x|| 
\               \2     //
1csc⁡(−x+π2)−2csc⁡3(x)(−1+2csc⁡(x)csc⁡(−x+π2))2\frac{\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{2}{\csc^{3}{\left(x \right)}}}{\left(-1 + \frac{2}{\csc{\left(x \right)} \csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{2}} 
       3            
- 2*sin (x) + cos(x)
--------------------
                 2  
  (-1 + sin(2*x))
−2sin⁡3(x)+cos⁡(x)(sin⁡(2x)−1)2\frac{- 2 \sin^{3}{\left(x \right)} + \cos{\left(x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} 
                                  /    pi\
                    2*cos(2*x)*cos|x - --|
      cos(x)                      \    2 /
----------------- + ----------------------
       /      pi\                       2 
1 - cos|2*x - --|    /       /      pi\\  
       \      2 /    |1 - cos|2*x - --||  
                     \       \      2 //
cos⁡(x)1−cos⁡(2x−π2)+2cos⁡(2x)cos⁡(x−π2)(1−cos⁡(2x−π2))2\frac{\cos{\left(x \right)}}{1 - \cos{\left(2 x - \frac{\pi}{2} \right)}} + \frac{2 \cos{\left(2 x \right)} \cos{\left(x - \frac{\pi}{2} \right)}}{\left(1 - \cos{\left(2 x - \frac{\pi}{2} \right)}\right)^{2}} 
     1            1           3    
----------- + ---------- - --------
   /pi    \   2*csc(3*x)   2*csc(x)
csc|-- - x|                        
   \2     /                        
-----------------------------------
                         2         
          /        1    \          
          |-1 + --------|          
          \     csc(2*x)/
1csc⁡(−x+π2)+12csc⁡(3x)−32csc⁡(x)(−1+1csc⁡(2x))2\frac{\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{2 \csc{\left(3 x \right)}} - \frac{3}{2 \csc{\left(x \right)}}}{\left(-1 + \frac{1}{\csc{\left(2 x \right)}}\right)^{2}} 
        2/x\         /3*x\            /x\ 
-1 + cot |-|      cot|---|       3*cot|-| 
         \2/         \ 2 /            \2/ 
------------ + ------------- - -----------
       2/x\           2/3*x\          2/x\
1 + cot |-|    1 + cot |---|   1 + cot |-|
        \2/            \ 2 /           \2/
------------------------------------------
                             2            
           /       2*cot(x) \             
           |-1 + -----------|             
           |            2   |             
           \     1 + cot (x)/
cot⁡2(x2)−1cot⁡2(x2)+1+cot⁡(3x2)cot⁡2(3x2)+1−3cot⁡(x2)cot⁡2(x2)+1(−1+2cot⁡(x)cot⁡2(x)+1)2\frac{\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\cot{\left(\frac{3 x}{2} \right)}}{\cot^{2}{\left(\frac{3 x}{2} \right)} + 1} - \frac{3 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}}{\left(-1 + \frac{2 \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1}\right)^{2}} 
          1                            2               
--------------------- + -------------------------------
/       1    \                        2                
|1 - --------|*sec(x)   /       1    \                 
\    csc(2*x)/          |1 - --------| *csc(x)*sec(2*x)
                        \    csc(2*x)/
1(1−1csc⁡(2x))sec⁡(x)+2(1−1csc⁡(2x))2csc⁡(x)sec⁡(2x)\frac{1}{\left(1 - \frac{1}{\csc{\left(2 x \right)}}\right) \sec{\left(x \right)}} + \frac{2}{\left(1 - \frac{1}{\csc{\left(2 x \right)}}\right)^{2} \csc{\left(x \right)} \sec{\left(2 x \right)}} 
sin(3*x)   3*sin(x)      /    pi\
-------- - -------- + sin|x + --|
   2          2          \    2 /
---------------------------------
                        2        
         (-1 + sin(2*x))
−3sin⁡(x)2+sin⁡(3x)2+sin⁡(x+π2)(sin⁡(2x)−1)2\frac{- \frac{3 \sin{\left(x \right)}}{2} + \frac{\sin{\left(3 x \right)}}{2} + \sin{\left(x + \frac{\pi}{2} \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} 
  -sin(3*x) + 3*sin(x)         
- -------------------- + cos(x)
           2                   
-------------------------------
                       2       
        (-1 + sin(2*x))
−3sin⁡(x)−sin⁡(3x)2+cos⁡(x)(sin⁡(2x)−1)2\frac{- \frac{3 \sin{\left(x \right)} - \sin{\left(3 x \right)}}{2} + \cos{\left(x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} 
         3             
  - 2*sin (x) + cos(x) 
-----------------------
                      2
(-1 + 2*cos(x)*sin(x))
−2sin⁡3(x)+cos⁡(x)(2sin⁡(x)cos⁡(x)−1)2\frac{- 2 \sin^{3}{\left(x \right)} + \cos{\left(x \right)}}{\left(2 \sin{\left(x \right)} \cos{\left(x \right)} - 1\right)^{2}} 
(-2*sin(x)^3 + cos(x))/(-1 + 2*cos(x)*sin(x))^2
Respuesta numérica [src] 
cos(x)/(1.0 - sin(2*x)) + 2.0*cos(2*x)*sin(x)/(1.0 - sin(2*x))^2
cos(x)/(1.0 - sin(2*x)) + 2.0*cos(2*x)*sin(x)/(1.0 - sin(2*x))^2
    © Sr Examen – Калькулятор