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¿cómo vas a descomponer esta expresión en fracciones?:
1/(3,94436∙〖10〗^(-7))
((3*c+1)/(c-1)+c)/(c+1)
-1/(5*x^5)
(49*b/a-25*a/b)/(7*a+5*b)
Factorizar el polinomio:
y^4-25
y^5-y^3-y+1
y^5+y+1
-y^3+y^2-1
Descomponer al cuadrado:
-y^4-8*y^2-8
-y^4+9*y^2-3
-y^4+8*y^2+4
-y^4-8*y^2-3
Expresiones idénticas
sin(x)^ dos *cos(x)/(dos -sin(x))^ dos + dos *cos(x)*sin(x)/(dos -sin(x))
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seno de (x) en el grado dos multiplicar por coseno de (x) dividir por (dos menos seno de (x)) en el grado dos más dos multiplicar por coseno de (x) multiplicar por seno de (x) dividir por (dos menos seno de (x))
sin(x)2*cos(x)/(2-sin(x))2+2*cos(x)*sin(x)/(2-sin(x))
sinx2*cosx/2-sinx2+2*cosx*sinx/2-sinx
sin(x)²*cos(x)/(2-sin(x))²+2*cos(x)*sin(x)/(2-sin(x))
sin(x) en el grado 2*cos(x)/(2-sin(x)) en el grado 2+2*cos(x)*sin(x)/(2-sin(x))
sin(x)^2cos(x)/(2-sin(x))^2+2cos(x)sin(x)/(2-sin(x))
sin(x)2cos(x)/(2-sin(x))2+2cos(x)sin(x)/(2-sin(x))
sinx2cosx/2-sinx2+2cosxsinx/2-sinx
sinx^2cosx/2-sinx^2+2cosxsinx/2-sinx
sin(x)^2*cos(x) dividir por (2-sin(x))^2+2*cos(x)*sin(x) dividir por (2-sin(x))
Expresiones semejantes
sin(x)^2*cos(x)/(2+sin(x))^2+2*cos(x)*sin(x)/(2-sin(x))
sin(x)^2*cos(x)/(2-sin(x))^2-2*cos(x)*sin(x)/(2-sin(x))
sin(x)^2*cos(x)/(2-sin(x))^2+2*cos(x)*sin(x)/(2+sin(x))
sinx^2*cosx/(2-sinx)^2+2*cosx*sinx/(2-sinx)
Expresiones con funciones
Seno sin
sin^2/(cos-1)
sin^2a(cos4a-cos2a)/(sina-2sin3a+sin5a)
sin20/(2*cos10)
sin(2*x)/(1+cos(2*x))
sin(x)/(2*sqrt(cos(x)))
Coseno cos
cos(10*a)/(sin(5*a)-cos(5*a))
cos(x)*(-sin(x)-(cos(x)*sin(x)))/sqrt(1+cos(x)^(2))/(cos(x)+sqrt(1+cos(x)^(2)))
cos(x)+t*sin(x)/(1-t*(x^2)/2)*x
cos(x)/(x+1)^3-3*sin(x)/(x+1)^4
cos(x)/(cos(x)+1)+sin(x)^2/(cos(x)+1)^2
Seno sin
sin^2/(cos-1)
sin^2a(cos4a-cos2a)/(sina-2sin3a+sin5a)
sin20/(2*cos10)
sin(2*x)/(1+cos(2*x))
sin(x)/(2*sqrt(cos(x)))
Coseno cos
cos(10*a)/(sin(5*a)-cos(5*a))
cos(x)*(-sin(x)-(cos(x)*sin(x)))/sqrt(1+cos(x)^(2))/(cos(x)+sqrt(1+cos(x)^(2)))
cos(x)+t*sin(x)/(1-t*(x^2)/2)*x
cos(x)/(x+1)^3-3*sin(x)/(x+1)^4
cos(x)/(cos(x)+1)+sin(x)^2/(cos(x)+1)^2
Seno sin
sin^2/(cos-1)
sin^2a(cos4a-cos2a)/(sina-2sin3a+sin5a)
sin20/(2*cos10)
sin(2*x)/(1+cos(2*x))
sin(x)/(2*sqrt(cos(x)))
Seno sin
sin^2/(cos-1)
sin^2a(cos4a-cos2a)/(sina-2sin3a+sin5a)
sin20/(2*cos10)
sin(2*x)/(1+cos(2*x))
sin(x)/(2*sqrt(cos(x)))

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

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

Solución

Ha introducido [src]

   2                            
sin (x)*cos(x)   2*cos(x)*sin(x)
-------------- + ---------------
            2       2 - sin(x)  
(2 - sin(x))

\frac{\sin{\left(x \right)} 2 \cos{\left(x \right)}}{2 - \sin{\left(x \right)}} + \frac{\sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\left(2 - \sin{\left(x \right)}\right)^{2}}

(sin(x)^2*cos(x))/(2 - sin(x))^2 + ((2*cos(x))*sin(x))/(2 - sin(x))

Simplificación general [src]

(4 - sin(x))*cos(x)*sin(x)
--------------------------
                   2      
      (-2 + sin(x))

\frac{\left(4 - \sin{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\left(\sin{\left(x \right)} - 2\right)^{2}}

(4 - sin(x))*cos(x)*sin(x)/(-2 + sin(x))^2

Respuesta numérica [src]

0.25*sin(x)^2*cos(x)/(1 - 0.5*sin(x))^2 + 2.0*cos(x)*sin(x)/(2.0 - sin(x))

0.25*sin(x)^2*cos(x)/(1 - 0.5*sin(x))^2 + 2.0*cos(x)*sin(x)/(2.0 - sin(x))

Unión de expresiones racionales [src]

(4 - sin(x))*cos(x)*sin(x)
--------------------------
                  2       
      (2 - sin(x))

\frac{\left(4 - \sin{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\left(2 - \sin{\left(x \right)}\right)^{2}}

(4 - sin(x))*cos(x)*sin(x)/(2 - sin(x))^2

Combinatoria [src]

-(-4 + sin(x))*cos(x)*sin(x) 
-----------------------------
                     2       
        (-2 + sin(x))

- \frac{\left(\sin{\left(x \right)} - 4\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\left(\sin{\left(x \right)} - 2\right)^{2}}

-(-4 + sin(x))*cos(x)*sin(x)/(-2 + sin(x))^2

Denominador racional [src]

   2                                        2              
sin (x)*(2 - sin(x))*cos(x) + 2*(2 - sin(x)) *cos(x)*sin(x)
-----------------------------------------------------------
                                   3                       
                       (2 - sin(x))

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

(sin(x)^2*(2 - sin(x))*cos(x) + 2*(2 - sin(x))^2*cos(x)*sin(x))/(2 - sin(x))^3

Denominador común [src]

                 4*cos(x)       
-cos(x) + ----------------------
                 2              
          4 + sin (x) - 4*sin(x)

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

-cos(x) + 4*cos(x)/(4 + sin(x)^2 - 4*sin(x))

Potencias [src]

                  2 / I*x    -I*x\                                    
  /   -I*x    I*x\  |e      e    |                                    
  \- e     + e   / *|---- + -----|     /   -I*x    I*x\ / I*x    -I*x\
                    \ 2       2  /   I*\- e     + e   /*\e    + e    /
- -------------------------------- - ---------------------------------
                              2            /      /   -I*x    I*x\\   
      /      /   -I*x    I*x\\             |    I*\- e     + e   /|   
      |    I*\- e     + e   /|           2*|2 + ------------------|   
    4*|2 + ------------------|             \            2         /   
      \            2         /

- \frac{i \left(e^{i x} - e^{- i x}\right) \left(e^{i x} + e^{- i x}\right)}{2 \left(\frac{i \left(e^{i x} - e^{- i x}\right)}{2} + 2\right)} - \frac{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \left(e^{i x} - e^{- i x}\right)^{2}}{4 \left(\frac{i \left(e^{i x} - e^{- i x}\right)}{2} + 2\right)^{2}}

   2                            
sin (x)*cos(x)   2*cos(x)*sin(x)
-------------- + ---------------
            2       2 - sin(x)  
(2 - sin(x))

\frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{2 - \sin{\left(x \right)}} + \frac{\sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\left(2 - \sin{\left(x \right)}\right)^{2}}

sin(x)^2*cos(x)/(2 - sin(x))^2 + 2*cos(x)*sin(x)/(2 - sin(x))

Abrimos la expresión [src]

                         2              
2*cos(x)*sin(x)       sin (x)*cos(x)    
--------------- + ----------------------
   2 - sin(x)            2              
                  4 + sin (x) - 4*sin(x)

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

((2*cos(x))*sin(x))/(2 - sin(x)) + sin(x)^2*cos(x)/(4 + sin(x)^2 - 4*sin(x))

Compilar la expresión [src]

   2                            
sin (x)*cos(x)   2*cos(x)*sin(x)
-------------- + ---------------
            2       2 - sin(x)  
(2 - sin(x))

\frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{2 - \sin{\left(x \right)}} + \frac{\sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\left(2 - \sin{\left(x \right)}\right)^{2}}

sin(x)^2*cos(x)/(2 - sin(x))^2 + 2*cos(x)*sin(x)/(2 - sin(x))

Parte trigonométrica [src]

                     6                                           4                  
       /        2/x\\  /       1   \               /        2/x\\  /       1   \    
     4*|-1 + cot |-|| *|1 - -------|             4*|-1 + cot |-|| *|1 - -------|    
       \         \4//  |       2/x\|               \         \4//  |       2/x\|    
                       |    cot |-||                               |    cot |-||    
                       \        \2//                               \        \2//    
------------------------------------------ + ---------------------------------------
                                 2                          /           /x\ \       
               /            /x\ \                         4 |      2*cot|-| |       
             6 |       2*cot|-| |            /       2/x\\  |           \2/ |    /x\
/       2/x\\  |            \2/ |     2/x\   |1 + cot |-|| *|2 - -----------|*cot|-|
|1 + cot |-|| *|-2 + -----------| *cot |-|   \        \4//  |           2/x\|    \2/
\        \4//  |            2/x\|      \2/                  |    1 + cot |-||       
               |     1 + cot |-||                           \            \2//       
               \             \2//

\frac{4 \left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{4}}{\left(2 - \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4} \cot{\left(\frac{x}{2} \right)}} + \frac{4 \left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{6}}{\left(-2 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{2} \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{6} \cot^{2}{\left(\frac{x}{2} \right)}}

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

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

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

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

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

\frac{\left(- \sin^{2}{\left(\frac{x}{2} \right)} + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{2}{\left(\frac{x}{2} \right)}}\right) \sin^{2}{\left(x \right)}}{\left(\sin{\left(x \right)} - 2\right)^{2}} - \frac{\sin{\left(2 x \right)}}{\sin{\left(x \right)} - 2}

               4                                               6                               
  /       2/x\\     8/x\ /       2/x\\    /x\     /       2/x\\     12/x\    2/x\ /       2/x\\
4*|1 - tan |-|| *cos |-|*|1 - tan |-||*tan|-|   4*|1 - tan |-|| *cos  |-|*tan |-|*|1 - tan |-||
  \        \4//      \4/ \        \2//    \2/     \        \4//       \4/     \2/ \        \2//
--------------------------------------------- + -----------------------------------------------
                  2 - sin(x)                                                  2                
                                                                 (-2 + sin(x))

\frac{4 \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{6} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \cos^{12}{\left(\frac{x}{4} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\left(\sin{\left(x \right)} - 2\right)^{2}} + \frac{4 \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{4} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \cos^{8}{\left(\frac{x}{4} \right)} \tan{\left(\frac{x}{2} \right)}}{2 - \sin{\left(x \right)}}

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

\frac{2 \cos{\left(x \right)} \cos{\left(x - \frac{\pi}{2} \right)}}{2 - \cos{\left(x - \frac{\pi}{2} \right)}} + \frac{\cos{\left(x \right)} \cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\left(2 - \cos{\left(x - \frac{\pi}{2} \right)}\right)^{2}}

                4                                                6                               
  /        2/x\\     8/x\ /       2/x\\    /x\     /        2/x\\     12/x\    2/x\ /       2/x\\
4*|-1 + cot |-|| *sin |-|*|1 - tan |-||*tan|-|   4*|-1 + cot |-|| *sin  |-|*tan |-|*|1 - tan |-||
  \         \4//      \4/ \        \2//    \2/     \         \4//       \4/     \2/ \        \2//
---------------------------------------------- + ------------------------------------------------
                  2 - sin(x)                                                   2                 
                                                                  (-2 + sin(x))

\frac{4 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{6} \sin^{12}{\left(\frac{x}{4} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\left(\sin{\left(x \right)} - 2\right)^{2}} + \frac{4 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{4} \sin^{8}{\left(\frac{x}{4} \right)} \tan{\left(\frac{x}{2} \right)}}{2 - \sin{\left(x \right)}}

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

\frac{\left(4 - \cos{\left(x - \frac{\pi}{2} \right)}\right) \cos{\left(x \right)} \cos{\left(x - \frac{\pi}{2} \right)}}{\left(\cos{\left(x - \frac{\pi}{2} \right)} - 2\right)^{2}}

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

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

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

\frac{2 \left(- \sin{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} \right)} + \sin{\left(x \right)} - 2\right) \sin^{2}{\left(\frac{x}{2} \right)} \sin{\left(2 x \right)}}{\left(\sin{\left(x \right)} - 2\right)^{2} \left(\cos{\left(x \right)} - 1\right)}

             1                             2             
---------------------------- + --------------------------
            2                  /      1   \              
/      1   \     2             |2 - ------|*csc(x)*sec(x)
|2 - ------| *csc (x)*sec(x)   \    csc(x)/              
\    csc(x)/

\frac{2}{\left(2 - \frac{1}{\csc{\left(x \right)}}\right) \csc{\left(x \right)} \sec{\left(x \right)}} + \frac{1}{\left(2 - \frac{1}{\csc{\left(x \right)}}\right)^{2} \csc^{2}{\left(x \right)} \sec{\left(x \right)}}

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

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

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

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

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

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

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

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

                       /         4/x\\                           /         4/x\\
                       |    4*sin |-||                           |    4*sin |-||
     2/x\    4/pi   x\ |          \2/|         4/x\    6/pi   x\ |          \2/|
8*sin |-|*sin |-- + -|*|1 - ---------|   16*sin |-|*sin |-- + -|*|1 - ---------|
      \2/     \2    2/ |        2    |          \2/     \2    2/ |        2    |
                       \     sin (x) /                           \     sin (x) /
-------------------------------------- + ---------------------------------------
         (2 - sin(x))*sin(x)                                   2    2           
                                                  (-2 + sin(x)) *sin (x)

\frac{16 \left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \sin^{4}{\left(\frac{x}{2} \right)} \sin^{6}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}}{\left(\sin{\left(x \right)} - 2\right)^{2} \sin^{2}{\left(x \right)}} + \frac{8 \left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \sin^{2}{\left(\frac{x}{2} \right)} \sin^{4}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}}{\left(2 - \sin{\left(x \right)}\right) \sin{\left(x \right)}}

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

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

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

\frac{2 \sin{\left(x \right)} \sin{\left(x + \frac{\pi}{2} \right)}}{2 - \sin{\left(x \right)}} + \frac{\sin^{2}{\left(x \right)} \sin{\left(x + \frac{\pi}{2} \right)}}{\left(2 - \sin{\left(x \right)}\right)^{2}}

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

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

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

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

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

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

                 /           /x\ \       
                 |      2*cot|-| |       
  /        2/x\\ |           \2/ |    /x\
2*|-1 + cot |-||*|4 - -----------|*cot|-|
  \         \2// |           2/x\|    \2/
                 |    1 + cot |-||       
                 \            \2//       
-----------------------------------------
                                     2   
                   /            /x\ \    
                 2 |       2*cot|-| |    
    /       2/x\\  |            \2/ |    
    |1 + cot |-|| *|-2 + -----------|    
    \        \2//  |            2/x\|    
                   |     1 + cot |-||    
                   \             \2//

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

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

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

      4/x\    8/x\ /        2/x\\    /x\          2/x\    6/x\    12/x\ /        2/x\\
64*cot |-|*sin |-|*|-1 + cot |-||*cot|-|   256*cot |-|*cot |-|*sin  |-|*|-1 + cot |-||
       \4/     \4/ \         \2//    \2/           \2/     \4/      \4/ \         \2//
---------------------------------------- + -------------------------------------------
               2 - sin(x)                                              2              
                                                          (-2 + sin(x))

\frac{256 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \sin^{12}{\left(\frac{x}{4} \right)} \cot^{6}{\left(\frac{x}{4} \right)} \cot^{2}{\left(\frac{x}{2} \right)}}{\left(\sin{\left(x \right)} - 2\right)^{2}} + \frac{64 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \sin^{8}{\left(\frac{x}{4} \right)} \cot^{4}{\left(\frac{x}{4} \right)} \cot{\left(\frac{x}{2} \right)}}{2 - \sin{\left(x \right)}}

      4/x\ /        2/x\\    /x\          2/x\    6/x\ /        2/x\\
64*cot |-|*|-1 + cot |-||*cot|-|   256*cot |-|*cot |-|*|-1 + cot |-||
       \4/ \         \2//    \2/           \2/     \4/ \         \2//
-------------------------------- + ----------------------------------
               /           /x\ \                                    2
             4 |      2*cot|-| |                  /            /x\ \ 
/       2/x\\  |           \2/ |                6 |       2*cot|-| | 
|1 + cot |-|| *|2 - -----------|   /       2/x\\  |            \2/ | 
\        \4//  |           2/x\|   |1 + cot |-|| *|-2 + -----------| 
               |    1 + cot |-||   \        \4//  |            2/x\| 
               \            \2//                  |     1 + cot |-|| 
                                                  \             \2//

\frac{64 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \cot^{4}{\left(\frac{x}{4} \right)} \cot{\left(\frac{x}{2} \right)}}{\left(2 - \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4}} + \frac{256 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \cot^{6}{\left(\frac{x}{4} \right)} \cot^{2}{\left(\frac{x}{2} \right)}}{\left(-2 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{2} \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{6}}

                /           /x\ \       
                |      2*tan|-| |       
  /       2/x\\ |           \2/ |    /x\
2*|1 - tan |-||*|4 - -----------|*tan|-|
  \        \2// |           2/x\|    \2/
                |    1 + tan |-||       
                \            \2//       
----------------------------------------
                                    2   
                  /            /x\ \    
                2 |       2*tan|-| |    
   /       2/x\\  |            \2/ |    
   |1 + tan |-|| *|-2 + -----------|    
   \        \2//  |            2/x\|    
                  |     1 + tan |-||    
                  \             \2//

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

               6                                        4                     
  /       2/x\\     2/x\ /       2/x\\     /       2/x\\  /       2/x\\    /x\
4*|1 - tan |-|| *tan |-|*|1 - tan |-||   4*|1 - tan |-|| *|1 - tan |-||*tan|-|
  \        \4//      \2/ \        \2//     \        \4//  \        \2//    \2/
-------------------------------------- + -------------------------------------
                                   2                       /           /x\ \  
                 /            /x\ \                      4 |      2*tan|-| |  
               6 |       2*tan|-| |         /       2/x\\  |           \2/ |  
  /       2/x\\  |            \2/ |         |1 + tan |-|| *|2 - -----------|  
  |1 + tan |-|| *|-2 + -----------|         \        \4//  |           2/x\|  
  \        \4//  |            2/x\|                        |    1 + tan |-||  
                 |     1 + tan |-||                        \            \2//  
                 \             \2//

\frac{4 \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{4} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \tan{\left(\frac{x}{2} \right)}}{\left(2 - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4}} + \frac{4 \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{6} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \tan^{2}{\left(\frac{x}{2} \right)}}{\left(-2 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{2} \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{6}}

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

\frac{2 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(4 - \sin{\left(x \right)}\right) \cos^{4}{\left(\frac{x}{2} \right)} \tan{\left(\frac{x}{2} \right)}}{\left(\sin{\left(x \right)} - 2\right)^{2}}

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

\frac{\left(4 - \sin{\left(x \right)}\right) \sin{\left(x \right)} \sin{\left(x + \frac{\pi}{2} \right)}}{\left(\sin{\left(x \right)} - 2\right)^{2}}

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

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

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

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

             cos(x)   cos(3*x)
2*sin(2*x) - ------ + --------
               4         4    
------------------------------
                     2        
        (-2 + sin(x))

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

   2                            
sin (x)*cos(x)   2*cos(x)*sin(x)
-------------- + ---------------
            2       2 - sin(x)  
(2 - sin(x))

\frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{2 - \sin{\left(x \right)}} + \frac{\sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\left(2 - \sin{\left(x \right)}\right)^{2}}

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

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

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

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

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

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

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

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

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

\frac{2 \left(4 - \sin{\left(x \right)}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \sin^{4}{\left(\frac{x}{2} \right)} \cot{\left(\frac{x}{2} \right)}}{\left(\sin{\left(x \right)} - 2\right)^{2}}

             4/x\ /        1   \                         6/x\ /        1   \        
       64*tan |-|*|-1 + -------|                  256*tan |-|*|-1 + -------|        
              \4/ |        2/x\|                          \4/ |        2/x\|        
                  |     tan |-||                              |     tan |-||        
                  \         \2//                              \         \2//        
--------------------------------------- + ------------------------------------------
               /           /x\ \                                           2        
             4 |      2*tan|-| |                         /            /x\ \         
/       2/x\\  |           \2/ |    /x\                6 |       2*tan|-| |         
|1 + tan |-|| *|2 - -----------|*tan|-|   /       2/x\\  |            \2/ |     2/x\
\        \4//  |           2/x\|    \2/   |1 + tan |-|| *|-2 + -----------| *tan |-|
               |    1 + tan |-||          \        \4//  |            2/x\|      \2/
               \            \2//                         |     1 + tan |-||         
                                                         \             \2//

\frac{64 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \tan^{4}{\left(\frac{x}{4} \right)}}{\left(2 - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4} \tan{\left(\frac{x}{2} \right)}} + \frac{256 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \tan^{6}{\left(\frac{x}{4} \right)}}{\left(-2 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{2} \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{6} \tan^{2}{\left(\frac{x}{2} \right)}}

(4 - sin(x))*cos(x)*sin(x)
--------------------------
                   2      
      (-2 + sin(x))

\frac{\left(4 - \sin{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\left(\sin{\left(x \right)} - 2\right)^{2}}

      8/x\    4/x\ /        1   \          12/x\    6/x\ /        1   \
64*cos |-|*tan |-|*|-1 + -------|   256*cos  |-|*tan |-|*|-1 + -------|
       \4/     \4/ |        2/x\|            \4/     \4/ |        2/x\|
                   |     tan |-||                        |     tan |-||
                   \         \2//                        \         \2//
--------------------------------- + -----------------------------------
                       /x\                              2    2/x\      
       (2 - sin(x))*tan|-|                 (-2 + sin(x)) *tan |-|      
                       \2/                                    \2/

\frac{256 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \cos^{12}{\left(\frac{x}{4} \right)} \tan^{6}{\left(\frac{x}{4} \right)}}{\left(\sin{\left(x \right)} - 2\right)^{2} \tan^{2}{\left(\frac{x}{2} \right)}} + \frac{64 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \cos^{8}{\left(\frac{x}{4} \right)} \tan^{4}{\left(\frac{x}{4} \right)}}{\left(2 - \sin{\left(x \right)}\right) \tan{\left(\frac{x}{2} \right)}}

64*cos(x/4)^8*tan(x/4)^4*(-1 + tan(x/2)^(-2))/((2 - sin(x))*tan(x/2)) + 256*cos(x/4)^12*tan(x/4)^6*(-1 + tan(x/2)^(-2))/((-2 + sin(x))^2*tan(x/2)^2)

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