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¿Cómo vas a descomponer esta tan(a)/(1-tan(a)^(2))+cot(a)/(1-cot(2*a)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
   tan(a)        cot(a)   
----------- + ------------
       2      1 - cot(2*a)
1 - tan (a)               
$$\frac{\cot{\left(a \right)}}{1 - \cot{\left(2 a \right)}} + \frac{\tan{\left(a \right)}}{1 - \tan^{2}{\left(a \right)}}$$
tan(a)/(1 - tan(a)^2) + cot(a)/(1 - cot(2*a))
Simplificación general [src]
        1       tan(a)        
      ------ - --------       
      tan(a)   tan(2*a)       
------------------------------
/        2   \                
\-1 + tan (a)/*(-1 + cot(2*a))
$$\frac{- \frac{\tan{\left(a \right)}}{\tan{\left(2 a \right)}} + \frac{1}{\tan{\left(a \right)}}}{\left(\tan^{2}{\left(a \right)} - 1\right) \left(\cot{\left(2 a \right)} - 1\right)}$$
(1/tan(a) - tan(a)/tan(2*a))/((-1 + tan(a)^2)*(-1 + cot(2*a)))
Respuesta numérica [src]
tan(a)/(1.0 - tan(a)^2) + cot(a)/(1.0 - cot(2*a))
tan(a)/(1.0 - tan(a)^2) + cot(a)/(1.0 - cot(2*a))
Combinatoria [src]
 /                      2                            \ 
-\-cot(a) - tan(a) + tan (a)*cot(a) + cot(2*a)*tan(a)/ 
-------------------------------------------------------
       (1 + tan(a))*(-1 + cot(2*a))*(-1 + tan(a))      
$$- \frac{\tan^{2}{\left(a \right)} \cot{\left(a \right)} + \tan{\left(a \right)} \cot{\left(2 a \right)} - \tan{\left(a \right)} - \cot{\left(a \right)}}{\left(\tan{\left(a \right)} - 1\right) \left(\tan{\left(a \right)} + 1\right) \left(\cot{\left(2 a \right)} - 1\right)}$$
-(-cot(a) - tan(a) + tan(a)^2*cot(a) + cot(2*a)*tan(a))/((1 + tan(a))*(-1 + cot(2*a))*(-1 + tan(a)))
Denominador racional [src]
/       2   \                               
\1 - tan (a)/*cot(a) + (1 - cot(2*a))*tan(a)
--------------------------------------------
        /       2   \                       
        \1 - tan (a)/*(1 - cot(2*a))        
$$\frac{\left(1 - \tan^{2}{\left(a \right)}\right) \cot{\left(a \right)} + \left(1 - \cot{\left(2 a \right)}\right) \tan{\left(a \right)}}{\left(1 - \tan^{2}{\left(a \right)}\right) \left(1 - \cot{\left(2 a \right)}\right)}$$
((1 - tan(a)^2)*cot(a) + (1 - cot(2*a))*tan(a))/((1 - tan(a)^2)*(1 - cot(2*a)))
Unión de expresiones racionales [src]
/       2   \                               
\1 - tan (a)/*cot(a) + (1 - cot(2*a))*tan(a)
--------------------------------------------
        /       2   \                       
        \1 - tan (a)/*(1 - cot(2*a))        
$$\frac{\left(1 - \tan^{2}{\left(a \right)}\right) \cot{\left(a \right)} + \left(1 - \cot{\left(2 a \right)}\right) \tan{\left(a \right)}}{\left(1 - \tan^{2}{\left(a \right)}\right) \left(1 - \cot{\left(2 a \right)}\right)}$$
((1 - tan(a)^2)*cot(a) + (1 - cot(2*a))*tan(a))/((1 - tan(a)^2)*(1 - cot(2*a)))
Abrimos la expresión [src]
        cot(a)             tan(a)  
--------------------- + -----------
       1       cot(a)          2   
1 + -------- - ------   1 - tan (a)
    2*cot(a)     2                 
$$\frac{\cot{\left(a \right)}}{- \frac{\cot{\left(a \right)}}{2} + 1 + \frac{1}{2 \cot{\left(a \right)}}} + \frac{\tan{\left(a \right)}}{1 - \tan^{2}{\left(a \right)}}$$
cot(a)/(1 + 1/(2*cot(a)) - cot(a)/2) + tan(a)/(1 - tan(a)^2)
Parte trigonométrica [src]
                    ___ /       1    \    /      pi\
                  \/ 2 *|1 + --------|*sec|2*a + --|
    sec(2*a)            \    sec(2*a)/    \      4 /
--------------- - ----------------------------------
     /      pi\                   2                 
2*sec|2*a - --|                                     
     \      2 /                                     
$$- \frac{\sqrt{2} \left(1 + \frac{1}{\sec{\left(2 a \right)}}\right) \sec{\left(2 a + \frac{\pi}{4} \right)}}{2} + \frac{\sec{\left(2 a \right)}}{2 \sec{\left(2 a - \frac{\pi}{2} \right)}}$$
    1           cot(a)   
---------- + ------------
2*cot(2*a)   1 - cot(2*a)
$$\frac{1}{2 \cot{\left(2 a \right)}} + \frac{\cot{\left(a \right)}}{1 - \cot{\left(2 a \right)}}$$
             ___               
tan(2*a)   \/ 2 *(1 + cos(2*a))
-------- - --------------------
   2              /      pi\   
             2*cos|2*a + --|   
                  \      4 /   
$$- \frac{\sqrt{2} \left(\cos{\left(2 a \right)} + 1\right)}{2 \cos{\left(2 a + \frac{\pi}{4} \right)}} + \frac{\tan{\left(2 a \right)}}{2}$$
              ___ /       /pi      \\
   2        \/ 2 *|1 + sin|-- + 2*a||
sin (2*a)         \       \2       //
--------- - -------------------------
 sin(4*a)            /      3*pi\    
                2*sin|2*a + ----|    
                     \       4  /    
$$- \frac{\sqrt{2} \left(\sin{\left(2 a + \frac{\pi}{2} \right)} + 1\right)}{2 \sin{\left(2 a + \frac{3 \pi}{4} \right)}} + \frac{\sin^{2}{\left(2 a \right)}}{\sin{\left(4 a \right)}}$$
    ___    2                 2          
  \/ 2 *cos (a)         2*sin (a)       
- ------------- + ----------------------
     /      pi\   /       2   \         
  cos|2*a + --|   \1 - tan (a)/*sin(2*a)
     \      4 /                         
$$- \frac{\sqrt{2} \cos^{2}{\left(a \right)}}{\cos{\left(2 a + \frac{\pi}{4} \right)}} + \frac{2 \sin^{2}{\left(a \right)}}{\left(1 - \tan^{2}{\left(a \right)}\right) \sin{\left(2 a \right)}}$$
                           /            2   \                                      
    ___ /       2/    pi\\ |    -1 + cot (a)|                                      
  \/ 2 *|1 + cot |a + --||*|1 + ------------|              2/a\ /       2   \      
        \        \    8 // |           2    |         4*cot |-|*\1 + cot (a)/      
                           \    1 + cot (a) /               \2/                    
- ------------------------------------------- + -----------------------------------
               /        2/    pi\\                           2                     
             2*|-1 + cot |a + --||              /       2/a\\  /       1   \       
               \         \    8 //              |1 + cot |-|| *|1 - -------|*cot(a)
                                                \        \2//  |       2   |       
                                                               \    cot (a)/       
$$- \frac{\sqrt{2} \left(\frac{\cot^{2}{\left(a \right)} - 1}{\cot^{2}{\left(a \right)} + 1} + 1\right) \left(\cot^{2}{\left(a + \frac{\pi}{8} \right)} + 1\right)}{2 \left(\cot^{2}{\left(a + \frac{\pi}{8} \right)} - 1\right)} + \frac{4 \left(\cot^{2}{\left(a \right)} + 1\right) \cot^{2}{\left(\frac{a}{2} \right)}}{\left(1 - \frac{1}{\cot^{2}{\left(a \right)}}\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \cot{\left(a \right)}}$$
   /pi      \                                  
csc|-- - 2*a|                                  
   \2       /                csc(a)            
------------- + -------------------------------
  2*csc(2*a)    /       csc(2*a)  \    /pi    \
                |1 - -------------|*csc|-- - a|
                |       /pi      \|    \2     /
                |    csc|-- - 2*a||            
                \       \2       //            
$$\frac{\csc{\left(- 2 a + \frac{\pi}{2} \right)}}{2 \csc{\left(2 a \right)}} + \frac{\csc{\left(a \right)}}{\left(- \frac{\csc{\left(2 a \right)}}{\csc{\left(- 2 a + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- a + \frac{\pi}{2} \right)}}$$
          /pi    \                                         
       csc|-- - a|                                         
          \2     /                       csc(a)            
------------------------- + -------------------------------
/       2/pi    \\          /       csc(2*a)  \    /pi    \
|    csc |-- - a||          |1 - -------------|*csc|-- - a|
|        \2     /|          |       /pi      \|    \2     /
|1 - ------------|*csc(a)   |    csc|-- - 2*a||            
|         2      |          \       \2       //            
\      csc (a)   /                                         
$$\frac{\csc{\left(a \right)}}{\left(- \frac{\csc{\left(2 a \right)}}{\csc{\left(- 2 a + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- a + \frac{\pi}{2} \right)}}{\left(1 - \frac{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(a \right)}}\right) \csc{\left(a \right)}}$$
                                           2          
    ___    2       /      pi\         2*sin (a)       
- \/ 2 *cos (a)*sec|2*a + --| + ----------------------
                   \      4 /   /       2   \         
                                \1 - tan (a)/*sin(2*a)
$$- \sqrt{2} \cos^{2}{\left(a \right)} \sec{\left(2 a + \frac{\pi}{4} \right)} + \frac{2 \sin^{2}{\left(a \right)}}{\left(1 - \tan^{2}{\left(a \right)}\right) \sin{\left(2 a \right)}}$$
       sin(a)                  cos(a)       
-------------------- + ---------------------
/       2   \          /    cos(2*a)\       
|    sin (a)|          |1 - --------|*sin(a)
|1 - -------|*cos(a)   \    sin(2*a)/       
|       2   |                               
\    cos (a)/                               
$$\frac{\sin{\left(a \right)}}{\left(- \frac{\sin^{2}{\left(a \right)}}{\cos^{2}{\left(a \right)}} + 1\right) \cos{\left(a \right)}} + \frac{\cos{\left(a \right)}}{\left(1 - \frac{\cos{\left(2 a \right)}}{\sin{\left(2 a \right)}}\right) \sin{\left(a \right)}}$$
                                    /           2   \
             ___ /       2/    pi\\ |    1 - tan (a)|
           \/ 2 *|1 + tan |a + --||*|1 + -----------|
                 \        \    8 // |           2   |
tan(2*a)                            \    1 + tan (a)/
-------- - ------------------------------------------
   2                    /       2/    pi\\           
                      2*|1 - tan |a + --||           
                        \        \    8 //           
$$\frac{\tan{\left(2 a \right)}}{2} - \frac{\sqrt{2} \left(\frac{1 - \tan^{2}{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1} + 1\right) \left(\tan^{2}{\left(a + \frac{\pi}{8} \right)} + 1\right)}{2 \left(1 - \tan^{2}{\left(a + \frac{\pi}{8} \right)}\right)}$$
   tan(a)               1          
----------- + ---------------------
       2      /       1    \       
1 - tan (a)   |1 - --------|*tan(a)
              \    tan(2*a)/       
$$\frac{1}{\left(1 - \frac{1}{\tan{\left(2 a \right)}}\right) \tan{\left(a \right)}} + \frac{\tan{\left(a \right)}}{1 - \tan^{2}{\left(a \right)}}$$
                                      2            
    ___    2       /       pi\   2*sin (a)*csc(2*a)
- \/ 2 *cos (a)*csc|-2*a + --| + ------------------
                   \       4 /             2       
                                    1 - tan (a)    
$$- \sqrt{2} \cos^{2}{\left(a \right)} \csc{\left(- 2 a + \frac{\pi}{4} \right)} + \frac{2 \sin^{2}{\left(a \right)} \csc{\left(2 a \right)}}{1 - \tan^{2}{\left(a \right)}}$$
tan(2*a)      cot(a)   
-------- + ------------
   2       1 - cot(2*a)
$$\frac{\tan{\left(2 a \right)}}{2} + \frac{\cot{\left(a \right)}}{1 - \cot{\left(2 a \right)}}$$
                  ___ /          1      \    /       pi\
                \/ 2 *|1 + -------------|*csc|-2*a + --|
   /pi      \         |       /pi      \|    \       4 /
csc|-- - 2*a|         |    csc|-- - 2*a||               
   \2       /         \       \2       //               
------------- - ----------------------------------------
  2*csc(2*a)                       2                    
$$- \frac{\sqrt{2} \left(1 + \frac{1}{\csc{\left(- 2 a + \frac{\pi}{2} \right)}}\right) \csc{\left(- 2 a + \frac{\pi}{4} \right)}}{2} + \frac{\csc{\left(- 2 a + \frac{\pi}{2} \right)}}{2 \csc{\left(2 a \right)}}$$
             /      pi\             ___ /       1    \    /      pi\
        2*sec|2*a - --|           \/ 2 *|1 + --------|*sec|2*a + --|
             \      2 /                 \    sec(2*a)/    \      4 /
------------------------------- - ----------------------------------
/         2      \                                2                 
|      sec (a)   |    2/    pi\                                     
|1 - ------------|*sec |a - --|                                     
|       2/    pi\|     \    2 /                                     
|    sec |a - --||                                                  
\        \    2 //                                                  
$$- \frac{\sqrt{2} \left(1 + \frac{1}{\sec{\left(2 a \right)}}\right) \sec{\left(2 a + \frac{\pi}{4} \right)}}{2} + \frac{2 \sec{\left(2 a - \frac{\pi}{2} \right)}}{\left(- \frac{\sec^{2}{\left(a \right)}}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} + 1\right) \sec^{2}{\left(a - \frac{\pi}{2} \right)}}$$
             ___    2    /       2/    pi\\
           \/ 2 *cos (a)*|1 + tan |a + --||
tan(2*a)                 \        \    8 //
-------- - --------------------------------
   2                      2/    pi\        
                   1 - tan |a + --|        
                           \    8 /        
$$\frac{\tan{\left(2 a \right)}}{2} - \frac{\sqrt{2} \left(\tan^{2}{\left(a + \frac{\pi}{8} \right)} + 1\right) \cos^{2}{\left(a \right)}}{1 - \tan^{2}{\left(a + \frac{\pi}{8} \right)}}$$
             ___    2   
tan(2*a)   \/ 2 *cos (a)
-------- - -------------
   2          /      pi\
           cos|2*a + --|
              \      4 /
$$- \frac{\sqrt{2} \cos^{2}{\left(a \right)}}{\cos{\left(2 a + \frac{\pi}{4} \right)}} + \frac{\tan{\left(2 a \right)}}{2}$$
                                          2           
          sin(2*a)                   2*sin (a)        
--------------------------- + ------------------------
  /      sin(4*a) \    2      /         4   \         
2*|1 - -----------|*sin (a)   |    4*sin (a)|         
  |         2     |           |1 - ---------|*sin(2*a)
  \    2*sin (2*a)/           |       2     |         
                              \    sin (2*a)/         
$$\frac{2 \sin^{2}{\left(a \right)}}{\left(- \frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} + 1\right) \sin{\left(2 a \right)}} + \frac{\sin{\left(2 a \right)}}{2 \left(1 - \frac{\sin{\left(4 a \right)}}{2 \sin^{2}{\left(2 a \right)}}\right) \sin^{2}{\left(a \right)}}$$
           2               ___               
      2*sin (a)          \/ 2 *(1 + cos(2*a))
---------------------- - --------------------
/       2   \                   /      pi\   
\1 - tan (a)/*sin(2*a)     2*cos|2*a + --|   
                                \      4 /   
$$- \frac{\sqrt{2} \left(\cos{\left(2 a \right)} + 1\right)}{2 \cos{\left(2 a + \frac{\pi}{4} \right)}} + \frac{2 \sin^{2}{\left(a \right)}}{\left(1 - \tan^{2}{\left(a \right)}\right) \sin{\left(2 a \right)}}$$
                      ___    2             
tan(2*a)            \/ 2 *cos (a)          
-------- - --------------------------------
   2       /        2/    pi\\    2/    pi\
           |-1 + cot |a + --||*sin |a + --|
           \         \    8 //     \    8 /
$$\frac{\tan{\left(2 a \right)}}{2} - \frac{\sqrt{2} \cos^{2}{\left(a \right)}}{\left(\cot^{2}{\left(a + \frac{\pi}{8} \right)} - 1\right) \sin^{2}{\left(a + \frac{\pi}{8} \right)}}$$
          /    pi\                                         
       cos|a - --|                                         
          \    2 /                       cos(a)            
------------------------- + -------------------------------
/       2/    pi\\          /       cos(2*a)  \    /    pi\
|    cos |a - --||          |1 - -------------|*cos|a - --|
|        \    2 /|          |       /      pi\|    \    2 /
|1 - ------------|*cos(a)   |    cos|2*a - --||            
|         2      |          \       \      2 //            
\      cos (a)   /                                         
$$\frac{\cos{\left(a \right)}}{\left(- \frac{\cos{\left(2 a \right)}}{\cos{\left(2 a - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(a - \frac{\pi}{2} \right)}} + \frac{\cos{\left(a - \frac{\pi}{2} \right)}}{\left(1 - \frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a \right)}}\right) \cos{\left(a \right)}}$$
              2/    pi\                                
         2*cos |a - --|              ___               
               \    2 /            \/ 2 *(1 + cos(2*a))
-------------------------------- - --------------------
/       2/    pi\\                        /      pi\   
|    cos |a - --||                   2*cos|2*a + --|   
|        \    2 /|    /      pi\          \      4 /   
|1 - ------------|*cos|2*a - --|                       
|         2      |    \      2 /                       
\      cos (a)   /                                     
$$- \frac{\sqrt{2} \left(\cos{\left(2 a \right)} + 1\right)}{2 \cos{\left(2 a + \frac{\pi}{4} \right)}} + \frac{2 \cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\left(1 - \frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a \right)}}\right) \cos{\left(2 a - \frac{\pi}{2} \right)}}$$
tan(2*a)             1          
-------- + ---------------------
   2       /       1    \       
           |1 - --------|*tan(a)
           \    tan(2*a)/       
$$\frac{\tan{\left(2 a \right)}}{2} + \frac{1}{\left(1 - \frac{1}{\tan{\left(2 a \right)}}\right) \tan{\left(a \right)}}$$
                                           /    pi\        
                                        sec|a - --|        
            sec(a)                         \    2 /        
------------------------------ + --------------------------
/         2      \               /       /      pi\\       
|      sec (a)   |    /    pi\   |    sec|2*a - --||       
|1 - ------------|*sec|a - --|   |       \      2 /|       
|       2/    pi\|    \    2 /   |1 - -------------|*sec(a)
|    sec |a - --||               \       sec(2*a)  /       
\        \    2 //                                         
$$\frac{\sec{\left(a \right)}}{\left(- \frac{\sec^{2}{\left(a \right)}}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(a - \frac{\pi}{2} \right)}} + \frac{\sec{\left(a - \frac{\pi}{2} \right)}}{\left(1 - \frac{\sec{\left(2 a - \frac{\pi}{2} \right)}}{\sec{\left(2 a \right)}}\right) \sec{\left(a \right)}}$$
   /      pi\                                  
cos|2*a - --|                                  
   \      2 /                cos(a)            
------------- + -------------------------------
  2*cos(2*a)    /       cos(2*a)  \    /    pi\
                |1 - -------------|*cos|a - --|
                |       /      pi\|    \    2 /
                |    cos|2*a - --||            
                \       \      2 //            
$$\frac{\cos{\left(2 a - \frac{\pi}{2} \right)}}{2 \cos{\left(2 a \right)}} + \frac{\cos{\left(a \right)}}{\left(- \frac{\cos{\left(2 a \right)}}{\cos{\left(2 a - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(a - \frac{\pi}{2} \right)}}$$
                                      /            2   \
               ___ /       2/    pi\\ |    -1 + cot (a)|
             \/ 2 *|1 + cot |a + --||*|1 + ------------|
                   \        \    8 // |           2    |
    1                                 \    1 + cot (a) /
---------- - -------------------------------------------
2*cot(2*a)                /        2/    pi\\           
                        2*|-1 + cot |a + --||           
                          \         \    8 //           
$$- \frac{\sqrt{2} \left(\frac{\cot^{2}{\left(a \right)} - 1}{\cot^{2}{\left(a \right)} + 1} + 1\right) \left(\cot^{2}{\left(a + \frac{\pi}{8} \right)} + 1\right)}{2 \left(\cot^{2}{\left(a + \frac{\pi}{8} \right)} - 1\right)} + \frac{1}{2 \cot{\left(2 a \right)}}$$
       sec(a)                  csc(a)       
-------------------- + ---------------------
/       2   \          /    csc(2*a)\       
|    sec (a)|          |1 - --------|*sec(a)
|1 - -------|*csc(a)   \    sec(2*a)/       
|       2   |                               
\    csc (a)/                               
$$\frac{\csc{\left(a \right)}}{\left(- \frac{\csc{\left(2 a \right)}}{\sec{\left(2 a \right)}} + 1\right) \sec{\left(a \right)}} + \frac{\sec{\left(a \right)}}{\left(1 - \frac{\sec^{2}{\left(a \right)}}{\csc^{2}{\left(a \right)}}\right) \csc{\left(a \right)}}$$
tan(2*a)     ___    2       /       pi\
-------- - \/ 2 *cos (a)*csc|-2*a + --|
   2                        \       4 /
$$- \sqrt{2} \cos^{2}{\left(a \right)} \csc{\left(- 2 a + \frac{\pi}{4} \right)} + \frac{\tan{\left(2 a \right)}}{2}$$
                           /           2   \                                      
    ___ /       2/    pi\\ |    1 - tan (a)|                                      
  \/ 2 *|1 + tan |a + --||*|1 + -----------|              2/a\ /       2   \      
        \        \    8 // |           2   |         4*tan |-|*\1 + tan (a)/      
                           \    1 + tan (a)/               \2/                    
- ------------------------------------------ + -----------------------------------
               /       2/    pi\\                           2                     
             2*|1 - tan |a + --||              /       2/a\\  /       2   \       
               \        \    8 //              |1 + tan |-|| *\1 - tan (a)/*tan(a)
                                               \        \2//                      
$$- \frac{\sqrt{2} \left(\frac{1 - \tan^{2}{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1} + 1\right) \left(\tan^{2}{\left(a + \frac{\pi}{8} \right)} + 1\right)}{2 \left(1 - \tan^{2}{\left(a + \frac{\pi}{8} \right)}\right)} + \frac{4 \left(\tan^{2}{\left(a \right)} + 1\right) \tan^{2}{\left(\frac{a}{2} \right)}}{\left(1 - \tan^{2}{\left(a \right)}\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan{\left(a \right)}}$$
         1                cot(a)   
-------------------- + ------------
/       1   \          1 - cot(2*a)
|1 - -------|*cot(a)               
|       2   |                      
\    cot (a)/                      
$$\frac{\cot{\left(a \right)}}{1 - \cot{\left(2 a \right)}} + \frac{1}{\left(1 - \frac{1}{\cot^{2}{\left(a \right)}}\right) \cot{\left(a \right)}}$$
   2                                   
sin (2*a)             sin(2*a)         
--------- + ---------------------------
 sin(4*a)     /      sin(4*a) \    2   
            2*|1 - -----------|*sin (a)
              |         2     |        
              \    2*sin (2*a)/        
$$\frac{\sin^{2}{\left(2 a \right)}}{\sin{\left(4 a \right)}} + \frac{\sin{\left(2 a \right)}}{2 \left(1 - \frac{\sin{\left(4 a \right)}}{2 \sin^{2}{\left(2 a \right)}}\right) \sin^{2}{\left(a \right)}}$$
                             ___ /       /pi      \\
            2              \/ 2 *|1 + sin|-- + 2*a||
       2*sin (a)                 \       \2       //
------------------------ - -------------------------
/         4   \                     /      3*pi\    
|    4*sin (a)|                2*sin|2*a + ----|    
|1 - ---------|*sin(2*a)            \       4  /    
|       2     |                                     
\    sin (2*a)/                                     
$$- \frac{\sqrt{2} \left(\sin{\left(2 a + \frac{\pi}{2} \right)} + 1\right)}{2 \sin{\left(2 a + \frac{3 \pi}{4} \right)}} + \frac{2 \sin^{2}{\left(a \right)}}{\left(- \frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} + 1\right) \sin{\left(2 a \right)}}$$
tan(2*a)     ___    2       /      pi\
-------- - \/ 2 *cos (a)*sec|2*a + --|
   2                        \      4 /
$$- \sqrt{2} \cos^{2}{\left(a \right)} \sec{\left(2 a + \frac{\pi}{4} \right)} + \frac{\tan{\left(2 a \right)}}{2}$$
   /      pi\                       
cos|2*a - --|     ___               
   \      2 /   \/ 2 *(1 + cos(2*a))
------------- - --------------------
  2*cos(2*a)           /      pi\   
                  2*cos|2*a + --|   
                       \      4 /   
$$- \frac{\sqrt{2} \left(\cos{\left(2 a \right)} + 1\right)}{2 \cos{\left(2 a + \frac{\pi}{4} \right)}} + \frac{\cos{\left(2 a - \frac{\pi}{2} \right)}}{2 \cos{\left(2 a \right)}}$$
                               ___ /          1      \    /       pi\
                             \/ 2 *|1 + -------------|*csc|-2*a + --|
                                   |       /pi      \|    \       4 /
                                   |    csc|-- - 2*a||               
        2*csc(2*a)                 \       \2       //               
-------------------------- - ----------------------------------------
/       2/pi    \\                              2                    
|    csc |-- - a||                                                   
|        \2     /|    2                                              
|1 - ------------|*csc (a)                                           
|         2      |                                                   
\      csc (a)   /                                                   
$$- \frac{\sqrt{2} \left(1 + \frac{1}{\csc{\left(- 2 a + \frac{\pi}{2} \right)}}\right) \csc{\left(- 2 a + \frac{\pi}{4} \right)}}{2} + \frac{2 \csc{\left(2 a \right)}}{\left(1 - \frac{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(a \right)}}\right) \csc^{2}{\left(a \right)}}$$
                            /    pi\        
                         sec|a - --|        
    sec(2*a)                \    2 /        
--------------- + --------------------------
     /      pi\   /       /      pi\\       
2*sec|2*a - --|   |    sec|2*a - --||       
     \      2 /   |       \      2 /|       
                  |1 - -------------|*sec(a)
                  \       sec(2*a)  /       
$$\frac{\sec{\left(2 a \right)}}{2 \sec{\left(2 a - \frac{\pi}{2} \right)}} + \frac{\sec{\left(a - \frac{\pi}{2} \right)}}{\left(1 - \frac{\sec{\left(2 a - \frac{\pi}{2} \right)}}{\sec{\left(2 a \right)}}\right) \sec{\left(a \right)}}$$
sec(2*a)/(2*sec(2*a - pi/2)) + sec(a - pi/2)/((1 - sec(2*a - pi/2)/sec(2*a))*sec(a))
Potencias [src]
                           /   I*a    -I*a\          
   cot(a)                I*\- e    + e    /          
------------ + --------------------------------------
1 - cot(2*a)   /                    2\               
               |    /   I*a    -I*a\ |               
               |    \- e    + e    / | / I*a    -I*a\
               |1 + -----------------|*\e    + e    /
               |                   2 |               
               |     / I*a    -I*a\  |               
               \     \e    + e    /  /               
$$\frac{i \left(- e^{i a} + e^{- i a}\right)}{\left(\frac{\left(- e^{i a} + e^{- i a}\right)^{2}}{\left(e^{i a} + e^{- i a}\right)^{2}} + 1\right) \left(e^{i a} + e^{- i a}\right)} + \frac{\cot{\left(a \right)}}{1 - \cot{\left(2 a \right)}}$$
cot(a)/(1 - cot(2*a)) + i*(-exp(i*a) + exp(-i*a))/((1 + (-exp(i*a) + exp(-i*a))^2/(exp(i*a) + exp(-i*a))^2)*(exp(i*a) + exp(-i*a)))
Denominador común [src]
 /                      2                            \ 
-\-cot(a) - tan(a) + tan (a)*cot(a) + cot(2*a)*tan(a)/ 
-------------------------------------------------------
              2                    2                   
       1 - tan (a) - cot(2*a) + tan (a)*cot(2*a)       
$$- \frac{\tan^{2}{\left(a \right)} \cot{\left(a \right)} + \tan{\left(a \right)} \cot{\left(2 a \right)} - \tan{\left(a \right)} - \cot{\left(a \right)}}{\tan^{2}{\left(a \right)} \cot{\left(2 a \right)} - \tan^{2}{\left(a \right)} - \cot{\left(2 a \right)} + 1}$$
-(-cot(a) - tan(a) + tan(a)^2*cot(a) + cot(2*a)*tan(a))/(1 - tan(a)^2 - cot(2*a) + tan(a)^2*cot(2*a))