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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
    2     
 sin (x)  
----------
cos(x) - 1
sin⁡2(x)cos⁡(x)−1\frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)} - 1} 
sin(x)^2/(cos(x) - 1)
Respuesta numérica [src] 
sin(x)^2/(-1.0 + cos(x))
sin(x)^2/(-1.0 + cos(x))
Potencias [src] 
                  2  
  /   -I*x    I*x\   
 -\- e     + e   /   
---------------------
  /      I*x    -I*x\
  |     e      e    |
4*|-1 + ---- + -----|
  \      2       2  /
−(eix−e−ix)24(eix2−1+e−ix2)- \frac{\left(e^{i x} - e^{- i x}\right)^{2}}{4 \left(\frac{e^{i x}}{2} - 1 + \frac{e^{- i x}}{2}\right)} 
-(-exp(-i*x) + exp(i*x))^2/(4*(-1 + exp(i*x)/2 + exp(-i*x)/2))
Parte trigonométrica [src] 
        /pi      \  
 1 - sin|-- + 2*x|  
        \2       /  
--------------------
  /        /    pi\\
2*|-1 + sin|x + --||
  \        \    2 //
1−sin⁡(2x+π2)2(sin⁡(x+π2)−1)\frac{1 - \sin{\left(2 x + \frac{\pi}{2} \right)}}{2 \left(\sin{\left(x + \frac{\pi}{2} \right)} - 1\right)} 
         1     
  1 - -------- 
      sec(2*x) 
---------------
  /       1   \
2*|-1 + ------|
  \     sec(x)/
1−1sec⁡(2x)2(−1+1sec⁡(x))\frac{1 - \frac{1}{\sec{\left(2 x \right)}}}{2 \left(-1 + \frac{1}{\sec{\left(x \right)}}\right)} 
            1             
--------------------------
/       1   \    2/    pi\
|-1 + ------|*sec |x - --|
\     sec(x)/     \    2 /
1(−1+1sec⁡(x))sec⁡2(x−π2)\frac{1}{\left(-1 + \frac{1}{\sec{\left(x \right)}}\right) \sec^{2}{\left(x - \frac{\pi}{2} \right)}} 
            1             
--------------------------
/          1     \    2   
|-1 + -----------|*csc (x)
|        /pi    \|        
|     csc|-- - x||        
\        \2     //
1(−1+1csc⁡(−x+π2))csc⁡2(x)\frac{1}{\left(-1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc^{2}{\left(x \right)}} 
  1 - cos(2*x) 
---------------
2*(-1 + cos(x))
1−cos⁡(2x)2(cos⁡(x)−1)\frac{1 - \cos{\left(2 x \right)}}{2 \left(\cos{\left(x \right)} - 1\right)} 
                 2/x\             
            4*cot |-|             
                  \2/             
----------------------------------
               /             2/x\\
             2 |     -1 + cot |-||
/       2/x\\  |              \2/|
|1 + cot |-|| *|-1 + ------------|
\        \2//  |            2/x\ |
               |     1 + cot |-| |
               \             \2/ /
4cot⁡2(x2)(cot⁡2(x2)−1cot⁡2(x2)+1−1)(cot⁡2(x2)+1)2\frac{4 \cot^{2}{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} 
   2/    pi\
cos |x - --|
    \    2 /
------------
-1 + cos(x)
cos⁡2(x−π2)cos⁡(x)−1\frac{\cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} - 1} 
                 2/x\            
            4*tan |-|            
                  \2/            
---------------------------------
               /            2/x\\
             2 |     1 - tan |-||
/       2/x\\  |             \2/|
|1 + tan |-|| *|-1 + -----------|
\        \2//  |            2/x\|
               |     1 + tan |-||
               \             \2//
4tan⁡2(x2)(1−tan⁡2(x2)tan⁡2(x2)+1−1)(tan⁡2(x2)+1)2\frac{4 \tan^{2}{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} 
           1        
 1 - -------------  
        /pi      \  
     csc|-- - 2*x|  
        \2       /  
--------------------
  /          1     \
2*|-1 + -----------|
  |        /pi    \|
  |     csc|-- - x||
  \        \2     //
1−1csc⁡(−2x+π2)2(−1+1csc⁡(−x+π2))\frac{1 - \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}}{2 \left(-1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)} 
       2        
    sin (x)     
----------------
        /    pi\
-1 + sin|x + --|
        \    2 /
sin⁡2(x)sin⁡(x+π2)−1\frac{\sin^{2}{\left(x \right)}}{\sin{\left(x + \frac{\pi}{2} \right)} - 1} 
          1          
---------------------
/       1   \    2   
|-1 + ------|*csc (x)
\     sec(x)/
1(−1+1sec⁡(x))csc⁡2(x)\frac{1}{\left(-1 + \frac{1}{\sec{\left(x \right)}}\right) \csc^{2}{\left(x \right)}} 
             2      
      1 - tan (x)   
  1 - -----------   
             2      
      1 + tan (x)   
--------------------
  /            2/x\\
  |     1 - tan |-||
  |             \2/|
2*|-1 + -----------|
  |            2/x\|
  |     1 + tan |-||
  \             \2//
−1−tan⁡2(x)tan⁡2(x)+1+12(1−tan⁡2(x2)tan⁡2(x2)+1−1)\frac{- \frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + 1}{2 \left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - 1\right)} 
               2     
       -1 + cot (x)  
   1 - ------------  
              2      
       1 + cot (x)   
---------------------
  /             2/x\\
  |     -1 + cot |-||
  |              \2/|
2*|-1 + ------------|
  |            2/x\ |
  |     1 + cot |-| |
  \             \2/ /
−cot⁡2(x)−1cot⁡2(x)+1+12(cot⁡2(x2)−1cot⁡2(x2)+1−1)\frac{- \frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} + 1}{2 \left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - 1\right)} 
(1 - (-1 + cot(x)^2)/(1 + cot(x)^2))/(2*(-1 + (-1 + cot(x/2)^2)/(1 + cot(x/2)^2)))
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