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Simplificación de expresiones/ Descomposición en fracciones simples/ tg^2*cosa/(1+ctg^2a)

¿Cómo vas a descomponer esta tg^2*cosa/(1+ctg^2a) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   2        
tan (cos(a))
------------
       2    
1 + cot (a)
$$\frac{\tan^{2}{\left(\cos{\left(a \right)} \right)}}{\cot^{2}{\left(a \right)} + 1}$$ 
tan(cos(a))^2/(1 + cot(a)^2)
Simplificación general [src] 
   2       2        
sin (a)*tan (cos(a))
$$\sin^{2}{\left(a \right)} \tan^{2}{\left(\cos{\left(a \right)} \right)}$$ 
sin(a)^2*tan(cos(a))^2
Respuesta numérica [src] 
tan(cos(a))^2/(1.0 + cot(a)^2)
tan(cos(a))^2/(1.0 + cot(a)^2)
Parte trigonométrica [src] 
             2/  1   \         
          sec |------|         
              \sec(a)/         
-------------------------------
/       2   \                  
|    csc (a)|    2/     1     \
|1 + -------|*csc |-----------|
|       2   |     |   /pi    \|
\    sec (a)/     |csc|-- - a||
                  \   \2     //
$$\frac{\sec^{2}{\left(\frac{1}{\sec{\left(a \right)}} \right)}}{\left(\frac{\csc^{2}{\left(a \right)}}{\sec^{2}{\left(a \right)}} + 1\right) \csc^{2}{\left(\frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} \right)}}$$ 
               2/  1   \            
            sec |------|            
                \sec(a)/            
------------------------------------
/       2/    pi\\                  
|    sec |a - --||                  
|        \    2 /|    2/  1      pi\
|1 + ------------|*sec |------ - --|
|         2      |     \sec(a)   2 /
\      sec (a)   /
$$\frac{\sec^{2}{\left(\frac{1}{\sec{\left(a \right)}} \right)}}{\left(1 + \frac{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)}}\right) \sec^{2}{\left(- \frac{\pi}{2} + \frac{1}{\sec{\left(a \right)}} \right)}}$$ 
        2/pi        1     \    
     csc |-- - -----------|    
         |2       /pi    \|    
         |     csc|-- - a||    
         \        \2     //    
-------------------------------
/         2      \             
|      csc (a)   |    2/  1   \
|1 + ------------|*csc |------|
|       2/pi    \|     \sec(a)/
|    csc |-- - a||             
\        \2     //
$$\frac{\csc^{2}{\left(\frac{\pi}{2} - \frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} \right)}}{\left(\frac{\csc^{2}{\left(a \right)}}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + 1\right) \csc^{2}{\left(\frac{1}{\sec{\left(a \right)}} \right)}}$$ 
              /       2/a\\
              |1 - tan |-||
     2/a\    2|        \2/|
4*tan |-|*tan |-----------|
      \2/     |       2/a\|
              |1 + tan |-||
              \        \2//
---------------------------
                    2      
       /       2/a\\       
       |1 + tan |-||       
       \        \2//
$$\frac{4 \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{1 - \tan^{2}{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}$$ 
                 2/a\            
            4*cot |-|            
                  \2/            
---------------------------------
                   /        2/a\\
             2     |-1 + cot |-||
/       2/a\\     2|         \2/|
|1 + cot |-|| *cot |------------|
\        \2//      |       2/a\ |
                   |1 + cot |-| |
                   \        \2/ /
$$\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \cot^{2}{\left(\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} \right)}}$$ 
         2/  pi         \      
      cos |- -- + cos(a)|      
          \  2          /      
-------------------------------
/         2      \             
|      cos (a)   |    2        
|1 + ------------|*cos (cos(a))
|       2/    pi\|             
|    cos |a - --||             
\        \    2 //
$$\frac{\cos^{2}{\left(\cos{\left(a \right)} - \frac{\pi}{2} \right)}}{\left(\frac{\cos^{2}{\left(a \right)}}{\cos^{2}{\left(a - \frac{\pi}{2} \right)}} + 1\right) \cos^{2}{\left(\cos{\left(a \right)} \right)}}$$ 
             4/   /    pi\\        
        4*sin |sin|a + --||        
              \   \    2 //        
-----------------------------------
/       2     \                    
|    sin (2*a)|    2/     /    pi\\
|1 + ---------|*sin |2*sin|a + --||
|         4   |     \     \    2 //
\    4*sin (a)/
$$\frac{4 \sin^{4}{\left(\sin{\left(a + \frac{\pi}{2} \right)} \right)}}{\left(1 + \frac{\sin^{2}{\left(2 a \right)}}{4 \sin^{4}{\left(a \right)}}\right) \sin^{2}{\left(2 \sin{\left(a + \frac{\pi}{2} \right)} \right)}}$$ 
          2               
       sin (cos(a))       
--------------------------
/       2   \             
|    cos (a)|    2        
|1 + -------|*cos (cos(a))
|       2   |             
\    sin (a)/
$$\frac{\sin^{2}{\left(\cos{\left(a \right)} \right)}}{\left(1 + \frac{\cos^{2}{\left(a \right)}}{\sin^{2}{\left(a \right)}}\right) \cos^{2}{\left(\cos{\left(a \right)} \right)}}$$ 
             4                
        4*sin (cos(a))        
------------------------------
/       2     \               
|    sin (2*a)|    2          
|1 + ---------|*sin (2*cos(a))
|         4   |               
\    4*sin (a)/
$$\frac{4 \sin^{4}{\left(\cos{\left(a \right)} \right)}}{\left(1 + \frac{\sin^{2}{\left(2 a \right)}}{4 \sin^{4}{\left(a \right)}}\right) \sin^{2}{\left(2 \cos{\left(a \right)} \right)}}$$ 
            2/  1   \         
         sec |------|         
             \sec(a)/         
------------------------------
   2/    pi\    2/  1      pi\
sec |a - --|*sec |------ - --|
    \    2 /     \sec(a)   2 /
$$\frac{\sec^{2}{\left(\frac{1}{\sec{\left(a \right)}} \right)}}{\sec^{2}{\left(- \frac{\pi}{2} + \frac{1}{\sec{\left(a \right)}} \right)} \sec^{2}{\left(a - \frac{\pi}{2} \right)}}$$ 
   2/    pi\    2/  pi         \
cos |a - --|*cos |- -- + cos(a)|
    \    2 /     \  2          /
--------------------------------
             2                  
          cos (cos(a))
$$\frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)} \cos^{2}{\left(\cos{\left(a \right)} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\cos{\left(a \right)} \right)}}$$ 
               1                
--------------------------------
                  /        2/a\\
                  |-1 + cot |-||
/       2   \    2|         \2/|
\1 + cot (a)/*cot |------------|
                  |       2/a\ |
                  |1 + cot |-| |
                  \        \2/ /
$$\frac{1}{\left(\cot^{2}{\left(a \right)} + 1\right) \cot^{2}{\left(\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} \right)}}$$ 
     2       4/   /    pi\\
4*sin (a)*sin |sin|a + --||
              \   \    2 //
---------------------------
       2/     /    pi\\    
    sin |2*sin|a + --||    
        \     \    2 //
$$\frac{4 \sin^{2}{\left(a \right)} \sin^{4}{\left(\sin{\left(a + \frac{\pi}{2} \right)} \right)}}{\sin^{2}{\left(2 \sin{\left(a + \frac{\pi}{2} \right)} \right)}}$$ 
   2/pi        1     \
csc |-- - -----------|
    |2       /pi    \|
    |     csc|-- - a||
    \        \2     //
----------------------
    2       2/  1   \ 
 csc (a)*csc |------| 
             \sec(a)/
$$\frac{\csc^{2}{\left(\frac{\pi}{2} - \frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} \right)}}{\csc^{2}{\left(a \right)} \csc^{2}{\left(\frac{1}{\sec{\left(a \right)}} \right)}}$$ 
    /       2/a\\
    |1 - tan |-||
   2|        \2/|
tan |-----------|
    |       2/a\|
    |1 + tan |-||
    \        \2//
-----------------
          1      
   1 + -------   
          2      
       tan (a)
$$\frac{\tan^{2}{\left(\frac{1 - \tan^{2}{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} \right)}}{1 + \frac{1}{\tan^{2}{\left(a \right)}}}$$ 
   2                       
tan (cos(a))*(1 - cos(2*a))
---------------------------
             2
$$\frac{\left(1 - \cos{\left(2 a \right)}\right) \tan^{2}{\left(\cos{\left(a \right)} \right)}}{2}$$ 
   2       2        
sin (a)*tan (cos(a))
$$\sin^{2}{\left(a \right)} \tan^{2}{\left(\cos{\left(a \right)} \right)}$$ 
sin(a)^2*tan(cos(a))^2
Potencias [src] 
                                                 2      
      /     / I*a    -I*a\      /   I*a    -I*a\\       
      |     |e      e    |      |  e      e    ||       
      |   I*|---- + -----|    I*|- ---- - -----||       
      |     \ 2       2  /      \   2       2  /|       
     -\- e                 + e                  /       
--------------------------------------------------------
                                                       2
              /   / I*a    -I*a\      /   I*a    -I*a\\ 
              |   |e      e    |      |  e      e    || 
              | I*|---- + -----|    I*|- ---- - -----|| 
/       2   \ |   \ 2       2  /      \   2       2  /| 
\1 + cot (a)/*\e                 + e                  /
$$- \frac{\left(e^{i \left(- \frac{e^{i a}}{2} - \frac{e^{- i a}}{2}\right)} - e^{i \left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right)}\right)^{2}}{\left(e^{i \left(- \frac{e^{i a}}{2} - \frac{e^{- i a}}{2}\right)} + e^{i \left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right)}\right)^{2} \left(\cot^{2}{\left(a \right)} + 1\right)}$$ 
-(-exp(i*(exp(i*a)/2 + exp(-i*a)/2)) + exp(i*(-exp(i*a)/2 - exp(-i*a)/2)))^2/((1 + cot(a)^2)*(exp(i*(exp(i*a)/2 + exp(-i*a)/2)) + exp(i*(-exp(i*a)/2 - exp(-i*a)/2)))^2)
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