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

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

Expresión a simplificar:

Solución

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