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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
      2       
   cos (x)    
--------------
   2          
sin (x)*cot(x)
$$\frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} \cot{\left(x \right)}}$$ 
cos(x)^2/((sin(x)^2*cot(x)))
Simplificación general [src] 
  1   
------
tan(x)
$$\frac{1}{\tan{\left(x \right)}}$$ 
1/tan(x)
Respuesta numérica [src] 
cos(x)^2/(cot(x)*sin(x)^2)
cos(x)^2/(cot(x)*sin(x)^2)
Potencias [src] 
                    2   
      / I*x    -I*x\    
      |e      e    |    
   -4*|---- + -----|    
      \ 2       2  /    
------------------------
                2       
/   -I*x    I*x\        
\- e     + e   / *cot(x)
$$- \frac{4 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}{\left(e^{i x} - e^{- i x}\right)^{2} \cot{\left(x \right)}}$$ 
-4*(exp(i*x)/2 + exp(-i*x)/2)^2/((-exp(-i*x) + exp(i*x))^2*cot(x))
Parte trigonométrica [src] 
                  2                    
/       2/pi   x\\                     
|    csc |-- - -||                     
|        \2    2/|     2/x\    /pi    \
|1 - ------------| *csc |-|*csc|-- - x|
|         2/x\   |      \2/    \2     /
|      csc |-|   |                     
\          \2/   /                     
---------------------------------------
                     2/pi   x\         
         4*csc(x)*csc |-- - -|         
                      \2    2/
$$\frac{\left(1 - \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \csc^{2}{\left(\frac{x}{2} \right)} \csc{\left(- x + \frac{\pi}{2} \right)}}{4 \csc{\left(x \right)} \csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}$$ 
cot(x)
$$\cot{\left(x \right)}$$ 
        sin(2*x)       
-----------------------
              2    2/x\
2*(1 + cos(x)) *tan |-|
                    \2/
$$\frac{\sin{\left(2 x \right)}}{2 \left(\cos{\left(x \right)} + 1\right)^{2} \tan^{2}{\left(\frac{x}{2} \right)}}$$ 
     2   
2*cos (x)
---------
 sin(2*x)
$$\frac{2 \cos^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}$$ 
cos(x)
------
sin(x)
$$\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$ 
 sin(2*x)
---------
     2   
2*sin (x)
$$\frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}}$$ 
                  2        
  /         2    \         
  |      sin (x) |     4/x\
2*|-1 + ---------| *sin |-|
  |          4/x\|      \2/
  |     4*sin |-||         
  \           \2//         
---------------------------
          sin(2*x)
$$\frac{2 \left(-1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right)^{2} \sin^{4}{\left(\frac{x}{2} \right)}}{\sin{\left(2 x \right)}}$$ 
                   2                         
/          2/x\   \                          
|       cos |-|   |                          
|           \2/   |     2/x   pi\    /    pi\
|-1 + ------------| *cos |- - --|*cos|x - --|
|        2/x   pi\|      \2   2 /    \    2 /
|     cos |- - --||                          
\         \2   2 //                          
---------------------------------------------
                           2/x\              
               4*cos(x)*cos |-|              
                            \2/
$$\frac{\left(\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - 1\right)^{2} \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)} \cos{\left(x - \frac{\pi}{2} \right)}}{4 \cos^{2}{\left(\frac{x}{2} \right)} \cos{\left(x \right)}}$$ 
   cos(x)  
-----------
   /    pi\
cos|x - --|
   \    2 /
$$\frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}}$$ 
csc(x)
------
sec(x)
$$\frac{\csc{\left(x \right)}}{\sec{\left(x \right)}}$$ 
                   2               
/        2/x   pi\\                
|     sec |- - --||                
|         \2   2 /|     2/x\       
|-1 + ------------| *sec |-|*sec(x)
|          2/x\   |      \2/       
|       sec |-|   |                
\           \2/   /                
-----------------------------------
          /    pi\    2/x   pi\    
     4*sec|x - --|*sec |- - --|    
          \    2 /     \2   2 /
$$\frac{\left(-1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \sec^{2}{\left(\frac{x}{2} \right)} \sec{\left(x \right)}}{4 \sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)} \sec{\left(x - \frac{\pi}{2} \right)}}$$ 
  1   
------
tan(x)
$$\frac{1}{\tan{\left(x \right)}}$$ 
   /    pi\
sec|x - --|
   \    2 /
-----------
   sec(x)
$$\frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}$$ 
             2       
/       2/x\\        
|1 - tan |-|| *tan(x)
\        \2//        
---------------------
           2/x\      
      4*tan |-|      
            \2/
$$\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \tan{\left(x \right)}}{4 \tan^{2}{\left(\frac{x}{2} \right)}}$$ 
             2        
/       1   \     2/x\
|1 - -------| *cot |-|
|       2/x\|      \2/
|    cot |-||         
\        \2//         
----------------------
       4*cot(x)
$$\frac{\left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \cot^{2}{\left(\frac{x}{2} \right)}}{4 \cot{\left(x \right)}}$$ 
     2/    pi\
2*sin |x + --|
      \    2 /
--------------
   sin(2*x)
$$\frac{2 \sin^{2}{\left(x + \frac{\pi}{2} \right)}}{\sin{\left(2 x \right)}}$$ 
                   2                         
/          2/x\   \                          
|       csc |-|   |                          
|           \2/   |     2/pi   x\    /pi    \
|-1 + ------------| *csc |-- - -|*csc|-- - x|
|        2/pi   x\|      \2    2/    \2     /
|     csc |-- - -||                          
\         \2    2//                          
---------------------------------------------
                           2/x\              
               4*csc(x)*csc |-|              
                            \2/
$$\frac{\left(\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - 1\right)^{2} \csc{\left(- x + \frac{\pi}{2} \right)} \csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{4 \csc^{2}{\left(\frac{x}{2} \right)} \csc{\left(x \right)}}$$ 
             2               
/       2/x\\     2/x\       
|1 - tan |-|| *cot |-|*tan(x)
\        \2//      \2/       
-----------------------------
              4
$$\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \tan{\left(x \right)} \cot^{2}{\left(\frac{x}{2} \right)}}{4}$$ 
              2               
/        1   \     2/x\       
|-1 + -------| *sin |-|*sin(x)
|        2/x\|      \2/       
|     tan |-||                
\         \2//                
------------------------------
    2*(1 + cos(x))*cos(x)
$$\frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \sin^{2}{\left(\frac{x}{2} \right)} \sin{\left(x \right)}}{2 \left(\cos{\left(x \right)} + 1\right) \cos{\left(x \right)}}$$ 
                  2                    
/       2/x   pi\\                     
|    cos |- - --||                     
|        \2   2 /|     2/x\    /    pi\
|1 - ------------| *cos |-|*cos|x - --|
|         2/x\   |      \2/    \    2 /
|      cos |-|   |                     
\          \2/   /                     
---------------------------------------
                     2/x   pi\         
         4*cos(x)*cos |- - --|         
                      \2   2 /
$$\frac{\left(1 - \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \cos^{2}{\left(\frac{x}{2} \right)} \cos{\left(x - \frac{\pi}{2} \right)}}{4 \cos{\left(x \right)} \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}$$ 
              2               
/        2/x\\     2/x\       
|-1 + cot |-|| *tan |-|*tan(x)
\         \2//      \2/       
------------------------------
              4
$$\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2} \tan^{2}{\left(\frac{x}{2} \right)} \tan{\left(x \right)}}{4}$$ 
                  2                    
/         2/x\   \                     
|      sec |-|   |                     
|          \2/   |     2/x   pi\       
|1 - ------------| *sec |- - --|*sec(x)
|       2/x   pi\|      \2   2 /       
|    sec |- - --||                     
\        \2   2 //                     
---------------------------------------
              2/x\    /    pi\         
         4*sec |-|*sec|x - --|         
               \2/    \    2 /
$$\frac{\left(- \frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2} \sec{\left(x \right)} \sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{4 \sec^{2}{\left(\frac{x}{2} \right)} \sec{\left(x - \frac{\pi}{2} \right)}}$$ 
   2/x\         
tan |-|*sin(2*x)
    \2/         
----------------
               2
2*(-1 + cos(x))
$$\frac{\sin{\left(2 x \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{2 \left(\cos{\left(x \right)} - 1\right)^{2}}$$ 
             2                      
/       2/x\\     2/x\              
|1 - tan |-|| *cos |-|*sec(x)*sin(x)
\        \2//      \2/              
------------------------------------
           2*(1 - cos(x))
$$\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \sin{\left(x \right)} \cos^{2}{\left(\frac{x}{2} \right)} \sec{\left(x \right)}}{2 \left(1 - \cos{\left(x \right)}\right)}$$ 
               2        
/         4/x\\         
|    4*sin |-||         
|          \2/|     4   
|1 - ---------| *sin (x)
|        2    |         
\     sin (x) /         
------------------------
        4/x\            
   8*sin |-|*sin(2*x)   
         \2/
$$\frac{\left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right)^{2} \sin^{4}{\left(x \right)}}{8 \sin^{4}{\left(\frac{x}{2} \right)} \sin{\left(2 x \right)}}$$ 
         2/x\   
   -2*sin |-|   
          \2/   
----------------
-tan(x) + sin(x)
$$- \frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{\sin{\left(x \right)} - \tan{\left(x \right)}}$$ 
              2 
/        2/x\\  
|-1 + cot |-||  
\         \2//  
----------------
            2/x\
4*cot(x)*cot |-|
             \2/
$$\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}{4 \cot^{2}{\left(\frac{x}{2} \right)} \cot{\left(x \right)}}$$ 
   csc(x)  
-----------
   /pi    \
csc|-- - x|
   \2     /
$$\frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}}$$ 
              2               
/        1   \     2/x\       
|-1 + -------| *tan |-|*tan(x)
|        2/x\|      \2/       
|     tan |-||                
\         \2//                
------------------------------
              4
$$\frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \tan^{2}{\left(\frac{x}{2} \right)} \tan{\left(x \right)}}{4}$$ 
(-1 + tan(x/2)^(-2))^2*tan(x/2)^2*tan(x)/4
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