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Factorizar el polinomio:
y^3+y
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Descomponer al cuadrado:
-y^4+8*y^2+2
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-y^4-7*y^2-9
y^4-7*y^2+4
Expresiones idénticas
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sin(x)/(tg(pi/4+x/2)(1+sin(x)))
sinx/tgpi/4+x/21+sinx
sin(x) dividir por (tg(pi dividir por 4+x dividir por 2)*(1+sin(x)))
Expresiones semejantes
sin(x)/(tg(pi/4-x/2)*(1+sin(x)))
sin(x)/(tg(pi/4+x/2)*(1-sin(x)))
sinx/(tg(pi/4+x/2)*(1+sinx))
Expresiones con funciones
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sin(x)^(sqrt(x))*(log(sin(x))/(2*sqrt(x))+sqrt(x)*cos(x)/sin(x))
sin(x+y)/(cosx*cosy)+tgy
tg
tg(7/(sqrt(3(n^4+2))))
tg4x/(1+tg4x*tg3x)
tg^2(x)*ctg^2(x)-(1-sin^2(5x))/(cos^2(5x)-1)
tg^2a-(1/(cos^2a))+sin^2a
tg4a*tg4a-(1-cos^29a)/(sin^29a)
Seno sin
sin(x+y)/((sin(x)*sin(y)))
sin(x)/(x-sin(x))+(-1+cos(x))*(2-cos(x))/(x-sin(x))^2
sin(x)*(sin(x)/(1-cos(x))-1/tan(x))
sin(x)^(sqrt(x))*(log(sin(x))/(2*sqrt(x))+sqrt(x)*cos(x)/sin(x))
sin(x+y)/(cosx*cosy)+tgy

Simplificación de expresiones/ Descomposición en fracciones simples/ sin(x)/(tg(pi/4+x/2)*(1+sin(x)))

¿Cómo vas a descomponer esta sin(x)/(tg(pi/4+x/2)*(1+sin(x))) expresión en fracciones?

Solución

Ha introducido [src]

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

\frac{\sin{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}

sin(x)/((tan(pi/4 + x/2)*(1 + sin(x))))

Respuesta numérica [src]

sin(x)/((1.0 + sin(x))*tan(pi/4 + x/2))

sin(x)/((1.0 + sin(x))*tan(pi/4 + x/2))

Potencias [src]

                       /   /x   pi\      /  x   pi\\      
                       | I*|- + --|    I*|- - - --||      
      /   -I*x    I*x\ |   \2   4 /      \  2   4 /|      
     -\- e     + e   /*\e           + e            /      
----------------------------------------------------------
                           /     /x   pi\      /  x   pi\\
  /      /   -I*x    I*x\\ |   I*|- + --|    I*|- - - --||
  |    I*\- e     + e   /| |     \2   4 /      \  2   4 /|
2*|1 - ------------------|*\- e           + e            /
  \            2         /

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

-(-exp(-i*x) + exp(i*x))*(exp(i*(x/2 + pi/4)) + exp(i*(-x/2 - pi/4)))/(2*(1 - i*(-exp(-i*x) + exp(i*x))/2)*(-exp(i*(x/2 + pi/4)) + exp(i*(-x/2 - pi/4))))

Denominador común [src]

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

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

sin(x)/(sin(x)*tan(x/2 + pi/4) + tan(x/2 + pi/4))

Unión de expresiones racionales [src]

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

\frac{\sin{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \tan{\left(\frac{2 x + \pi}{4} \right)}}

sin(x)/((1 + sin(x))*tan((pi + 2*x)/4))

Abrimos la expresión [src]

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

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

sin(x)/(1/(1 - tan(x/2)) + sin(x)/(1 - tan(x/2)) + tan(x/2)/(1 - tan(x/2)) + sin(x)*tan(x/2)/(1 - tan(x/2)))

Parte trigonométrica [src]

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

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

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

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

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

\frac{\left(1 + \frac{1}{\tan{\left(x \right)}} - \frac{1}{\sin{\left(x \right)}}\right) \sin{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \left(1 - \frac{1}{\tan{\left(x \right)}} + \frac{1}{\sin{\left(x \right)}}\right)}

     1 - cos(2*x)     
----------------------
              2       
2*(1 + sin(x)) *tan(x)

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

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

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

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

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

    sin(2*x)   
---------------
              2
2*(1 + sin(x))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\frac{\sin{\left(x \right)} \cos{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{\left(\sin{\left(x \right)} + 1\right) \sin{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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