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Simplificación de expresiones/ Descomposición en fracciones simples/ ((sin((3*pi)/2-a)^(2))+(cos((3*pi)/2-a)^(2)))/(cot(pi-a)^(2)*tan(pi-a)^(2))

¿Cómo vas a descomponer esta ((sin((3*pi)/2-a)^(2))+(cos((3*pi)/2-a)^(2)))/(cot(pi-a)^(2)*tan(pi-a)^(2)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   2/3*pi    \      2/3*pi    \
sin |---- - a| + cos |---- - a|
    \ 2      /       \ 2      /
-------------------------------
      2            2           
   cot (pi - a)*tan (pi - a)
$$\frac{\sin^{2}{\left(- a + \frac{3 \pi}{2} \right)} + \cos^{2}{\left(- a + \frac{3 \pi}{2} \right)}}{\tan^{2}{\left(\pi - a \right)} \cot^{2}{\left(\pi - a \right)}}$$ 
(sin((3*pi)/2 - a)^2 + cos((3*pi)/2 - a)^2)/((cot(pi - a)^2*tan(pi - a)^2))
Simplificación general [src] 
1
$$1$$ 
1
Respuesta numérica [src] 
(cos((3*pi)/2 - a)^2 + sin((3*pi)/2 - a)^2)/(cot(pi - a)^2*tan(pi - a)^2)
(cos((3*pi)/2 - a)^2 + sin((3*pi)/2 - a)^2)/(cot(pi - a)^2*tan(pi - a)^2)
Unión de expresiones racionales [src] 
   2/-2*a + 3*pi\      2/-2*a + 3*pi\
cos |-----------| + sin |-----------|
    \     2     /       \     2     /
-------------------------------------
              2       2              
           cot (a)*tan (a)
$$\frac{\sin^{2}{\left(\frac{- 2 a + 3 \pi}{2} \right)} + \cos^{2}{\left(\frac{- 2 a + 3 \pi}{2} \right)}}{\tan^{2}{\left(a \right)} \cot^{2}{\left(a \right)}}$$ 
(cos((-2*a + 3*pi)/2)^2 + sin((-2*a + 3*pi)/2)^2)/(cot(a)^2*tan(a)^2)
Denominador común [src] 
       2         2       
    cos (a) + sin (a)    
-------------------------
   2            2        
cot (pi - a)*tan (pi - a)
$$\frac{\sin^{2}{\left(a \right)} + \cos^{2}{\left(a \right)}}{\tan^{2}{\left(\pi - a \right)} \cot^{2}{\left(\pi - a \right)}}$$ 
(cos(a)^2 + sin(a)^2)/(cot(pi - a)^2*tan(pi - a)^2)
Combinatoria [src] 
   2         2   
cos (a) + sin (a)
-----------------
    2       2    
 cot (a)*tan (a)
$$\frac{\sin^{2}{\left(a \right)} + \cos^{2}{\left(a \right)}}{\tan^{2}{\left(a \right)} \cot^{2}{\left(a \right)}}$$ 
(cos(a)^2 + sin(a)^2)/(cot(a)^2*tan(a)^2)
Denominador racional [src] 
   2         2   
cos (a) + sin (a)
-----------------
    2       2    
 cot (a)*tan (a)
$$\frac{\sin^{2}{\left(a \right)} + \cos^{2}{\left(a \right)}}{\tan^{2}{\left(a \right)} \cot^{2}{\left(a \right)}}$$ 
(cos(a)^2 + sin(a)^2)/(cot(a)^2*tan(a)^2)
Abrimos la expresión [src] 
                    2       2                                            2       2                                                  2                                                    2                                                 2                                                    2                          
                 cos (a)*cot (a)                                      cot (a)*sin (a)                                        zoo*cos (a)                                          zoo*sin (a)                                       zoo*cos (a)*cot(a)                                   zoo*sin (a)*cot(a)                
-------------------------------------------------- + -------------------------------------------------- + -------------------------------------------------- + -------------------------------------------------- + -------------------------------------------------- + --------------------------------------------------
   2             2       2             2                2             2       2             2                2             2       2             2                2             2       2             2                2             2       2             2                2             2       2             2          
tan (a) + zoo*cot (a)*tan (a) + zoo*tan (a)*cot(a)   tan (a) + zoo*cot (a)*tan (a) + zoo*tan (a)*cot(a)   tan (a) + zoo*cot (a)*tan (a) + zoo*tan (a)*cot(a)   tan (a) + zoo*cot (a)*tan (a) + zoo*tan (a)*cot(a)   tan (a) + zoo*cot (a)*tan (a) + zoo*tan (a)*cot(a)   tan (a) + zoo*cot (a)*tan (a) + zoo*tan (a)*cot(a)
$$\frac{\sin^{2}{\left(a \right)} \cot^{2}{\left(a \right)}}{\tilde{\infty} \tan^{2}{\left(a \right)} \cot^{2}{\left(a \right)} + \tilde{\infty} \tan^{2}{\left(a \right)} \cot{\left(a \right)} + \tan^{2}{\left(a \right)}} + \frac{\tilde{\infty} \sin^{2}{\left(a \right)} \cot{\left(a \right)}}{\tilde{\infty} \tan^{2}{\left(a \right)} \cot^{2}{\left(a \right)} + \tilde{\infty} \tan^{2}{\left(a \right)} \cot{\left(a \right)} + \tan^{2}{\left(a \right)}} + \frac{\tilde{\infty} \sin^{2}{\left(a \right)}}{\tilde{\infty} \tan^{2}{\left(a \right)} \cot^{2}{\left(a \right)} + \tilde{\infty} \tan^{2}{\left(a \right)} \cot{\left(a \right)} + \tan^{2}{\left(a \right)}} + \frac{\cos^{2}{\left(a \right)} \cot^{2}{\left(a \right)}}{\tilde{\infty} \tan^{2}{\left(a \right)} \cot^{2}{\left(a \right)} + \tilde{\infty} \tan^{2}{\left(a \right)} \cot{\left(a \right)} + \tan^{2}{\left(a \right)}} + \frac{\tilde{\infty} \cos^{2}{\left(a \right)} \cot{\left(a \right)}}{\tilde{\infty} \tan^{2}{\left(a \right)} \cot^{2}{\left(a \right)} + \tilde{\infty} \tan^{2}{\left(a \right)} \cot{\left(a \right)} + \tan^{2}{\left(a \right)}} + \frac{\tilde{\infty} \cos^{2}{\left(a \right)}}{\tilde{\infty} \tan^{2}{\left(a \right)} \cot^{2}{\left(a \right)} + \tilde{\infty} \tan^{2}{\left(a \right)} \cot{\left(a \right)} + \tan^{2}{\left(a \right)}}$$ 
cos(a)^2*cot(a)^2/(tan(a)^2 + ±oo*cot(a)^2*tan(a)^2 + ±oo*tan(a)^2*cot(a)) + cot(a)^2*sin(a)^2/(tan(a)^2 + ±oo*cot(a)^2*tan(a)^2 + ±oo*tan(a)^2*cot(a)) + ±oo*cos(a)^2/(tan(a)^2 + ±oo*cot(a)^2*tan(a)^2 + ±oo*tan(a)^2*cot(a)) + ±oo*sin(a)^2/(tan(a)^2 + ±oo*cot(a)^2*tan(a)^2 + ±oo*tan(a)^2*cot(a)) + ±oo*cos(a)^2*cot(a)/(tan(a)^2 + ±oo*cot(a)^2*tan(a)^2 + ±oo*tan(a)^2*cot(a)) + ±oo*sin(a)^2*cot(a)/(tan(a)^2 + ±oo*cot(a)^2*tan(a)^2 + ±oo*tan(a)^2*cot(a))
Parte trigonométrica [src] 
                2    
    (1 + sin(a))     
---------------------
            4        
/       /a\\     4/a\
|1 + tan|-|| *cos |-|
\       \2//      \2/
$$\frac{\left(\sin{\left(a \right)} + 1\right)^{2}}{\left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{4} \cos^{4}{\left(\frac{a}{2} \right)}}$$ 
                                  2/a   pi\  
                             4*tan |- + --|  
       4/a\        2/a\            \2   4 /  
- 4*cos |-| + 4*cos |-| + -------------------
        \2/         \2/                     2
                          /       2/a   pi\\ 
                          |1 + tan |- + --|| 
                          \        \2   4 //
$$- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}$$ 
   2              2   
cos (pi - a) + sin (a)
$$\sin^{2}{\left(a \right)} + \cos^{2}{\left(\pi - a \right)}$$ 
                                                     2/a   pi\  
                                 4              4*tan |- + --|  
                   /        2/a\\     8/a\            \2   4 /  
2*(1 + cos(a)) - 4*|-1 + cot |-|| *sin |-| + -------------------
                   \         \4//      \4/                     2
                                             /       2/a   pi\\ 
                                             |1 + tan |- + --|| 
                                             \        \2   4 //
$$2 \left(\cos{\left(a \right)} + 1\right) - 4 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4} \sin^{8}{\left(\frac{a}{4} \right)} + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}$$ 
   1           1      
------- + ------------
   2         2/pi    \
sec (a)   sec |-- - a|
              \2     /
$$\frac{1}{\sec^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\sec^{2}{\left(a \right)}}$$ 
                  2                      
/       2/a   pi\\            2/a   pi\  
|1 - tan |- + --||       4*tan |- + --|  
\        \2   4 //             \2   4 /  
------------------- + -------------------
                  2                     2
/       2/a   pi\\    /       2/a   pi\\ 
|1 + tan |- + --||    |1 + tan |- + --|| 
\        \2   4 //    \        \2   4 //
$$\frac{\left(1 - \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}$$ 
   1           1      
------- + ------------
   2         2        
csc (a)   sec (pi - a)
$$\frac{1}{\sec^{2}{\left(\pi - a \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}$$ 
                                  2             
              /       2/  a   pi\\              
            2 |    csc |- - + --||              
/      1   \  |        \  2   4 /|     4/a   pi\
|1 + ------| *|1 + --------------| *csc |- + --|
\    csc(a)/  |        2/a   pi\ |      \2   4 /
              |     csc |- + --| |              
              \         \2   4 / /              
------------------------------------------------
                     4/  a   pi\                
                4*csc |- - + --|                
                      \  2   4 /
$$\frac{\left(1 + \frac{1}{\csc{\left(a \right)}}\right)^{2} \left(\frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + 1\right)^{2} \csc^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{4 \csc^{4}{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}$$ 
   2         2/    pi\
sin (a) + sin |a + --|
              \    2 /
$$\sin^{2}{\left(a \right)} + \sin^{2}{\left(a + \frac{\pi}{2} \right)}$$ 
                                        2/a   pi\         
                                   4*cos |- - --|         
       4/a\        2/a\                  \2   4 /         
- 4*cos |-| + 4*cos |-| + --------------------------------
        \2/         \2/                     2             
                          /       2/a   pi\\              
                          |    cos |- - --||              
                          |        \2   4 /|     2/a   pi\
                          |1 + ------------| *cos |- + --|
                          |       2/a   pi\|      \2   4 /
                          |    cos |- + --||              
                          \        \2   4 //
$$- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} + \frac{4 \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + 1\right)^{2} \cos^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}$$ 
   1           1      
------- + ------------
   2         2/pi    \
csc (a)   csc |-- - a|
              \2     /
$$\frac{1}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}$$ 
                                              2/  a   pi\         
                                         4*csc |- - + --|         
       4              4                        \  2   4 /         
- ------------ + ------------ + ----------------------------------
     4/pi   a\      2/pi   a\                       2             
  csc |-- - -|   csc |-- - -|   /       2/  a   pi\\              
      \2    2/       \2    2/   |    csc |- - + --||              
                                |        \  2   4 /|     2/a   pi\
                                |1 + --------------| *csc |- + --|
                                |        2/a   pi\ |      \2   4 /
                                |     csc |- + --| |              
                                \         \2   4 / /
$$\frac{4}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - \frac{4}{\csc^{4}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + \frac{4 \csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + 1\right)^{2} \csc^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}$$ 
                  2              
/       2/a   pi\\              2
|1 + tan |- + --|| *(1 + sin(a)) 
\        \2   4 //               
---------------------------------
               4/a   pi\         
          4*tan |- + --|         
                \2   4 /
$$\frac{\left(\sin{\left(a \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}{4 \tan^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}$$ 
                    2                      
/         4/a   pi\\                       
|    4*sin |- + --||                       
|          \2   4 /|              2    4   
|1 + --------------| *(1 + sin(a)) *cos (a)
|          2       |                       
\       cos (a)    /                       
-------------------------------------------
                    8/a   pi\              
              64*sin |- + --|              
                     \2   4 /
$$\frac{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cos^{2}{\left(a \right)}} + 1\right)^{2} \left(\sin{\left(a \right)} + 1\right)^{2} \cos^{4}{\left(a \right)}}{64 \sin^{8}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}$$ 
   1         1   
------- + -------
   2         2   
csc (a)   sec (a)
$$\frac{1}{\sec^{2}{\left(a \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}$$ 
                                     2
                    /           /a\ \ 
                  2 |      2*tan|-| | 
/       2/a   pi\\  |           \2/ | 
|1 + tan |- + --|| *|1 + -----------| 
\        \2   4 //  |           2/a\| 
                    |    1 + tan |-|| 
                    \            \2// 
--------------------------------------
                 4/a   pi\            
            4*tan |- + --|            
                  \2   4 /
$$\frac{\left(1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right)^{2} \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}{4 \tan^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}$$ 
                                     2             
                   /       2/a   pi\\              
                 2 |    sec |- + --||              
/         1     \  |        \2   4 /|     4/a   pi\
|1 + -----------| *|1 + ------------| *sec |- - --|
|       /    pi\|  |       2/a   pi\|      \2   4 /
|    sec|a - --||  |    sec |- - --||              
\       \    2 //  \        \2   4 //              
---------------------------------------------------
                        4/a   pi\                  
                   4*sec |- + --|                  
                         \2   4 /
$$\frac{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}\right)^{2} \left(1 + \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right)^{2} \sec^{4}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{4 \sec^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}$$ 
                                                    2/a   pi\  
                                4              4*tan |- + --|  
                   /       2/a\\     8/a\            \2   4 /  
2*(1 + cos(a)) - 4*|1 - tan |-|| *cos |-| + -------------------
                   \        \4//      \4/                     2
                                            /       2/a   pi\\ 
                                            |1 + tan |- + --|| 
                                            \        \2   4 //
$$- 4 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4} \cos^{8}{\left(\frac{a}{4} \right)} + 2 \left(\cos{\left(a \right)} + 1\right) + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}$$ 
                  2                                
/       2/a   pi\\                                 
|    cos |- - --||                   2             
|        \2   4 /|  /       /    pi\\     4/a   pi\
|1 + ------------| *|1 + cos|a - --|| *cos |- + --|
|       2/a   pi\|  \       \    2 //      \2   4 /
|    cos |- + --||                                 
\        \2   4 //                                 
---------------------------------------------------
                        4/a   pi\                  
                   4*cos |- - --|                  
                         \2   4 /
$$\frac{\left(\frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + 1\right)^{2} \left(\cos{\left(a - \frac{\pi}{2} \right)} + 1\right)^{2} \cos^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{4 \cos^{4}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}$$ 
1
$$1$$ 
   2         2           
cos (a) + sin (-a + 2*pi)
$$\sin^{2}{\left(- a + 2 \pi \right)} + \cos^{2}{\left(a \right)}$$ 
                  4                   2                                   
    /        2/a\\      /        2/a\\                                    
  4*|-1 + cot |-||    4*|-1 + cot |-||                                    
    \         \4//      \         \4//                   4                
- ----------------- + ----------------- + --------------------------------
                 4                   2                      2             
    /       2/a\\       /       2/a\\     /         1      \     2/a   pi\
    |1 + cot |-||       |1 + cot |-||     |1 + ------------| *cot |- + --|
    \        \4//       \        \4//     |       2/a   pi\|      \2   4 /
                                          |    cot |- + --||              
                                          \        \2   4 //
$$- \frac{4 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4}} + \frac{4 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}} + \frac{4}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right)^{2} \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}$$ 
   2         2/    pi\
cos (a) + cos |a - --|
              \    2 /
$$\cos^{2}{\left(a \right)} + \cos^{2}{\left(a - \frac{\pi}{2} \right)}$$ 
                   2                      
/        2/a   pi\\            2/a   pi\  
|-1 + cot |- + --||       4*cot |- + --|  
\         \2   4 //             \2   4 /  
-------------------- + -------------------
                  2                      2
/       2/a   pi\\     /       2/a   pi\\ 
|1 + cot |- + --||     |1 + cot |- + --|| 
\        \2   4 //     \        \2   4 //
$$\frac{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{4 \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}$$ 
                                    2/a   pi\         
                               4*sec |- + --|         
     4         4                     \2   4 /         
- ------- + ------- + --------------------------------
     4/a\      2/a\                     2             
  sec |-|   sec |-|   /       2/a   pi\\              
      \2/       \2/   |    sec |- + --||              
                      |        \2   4 /|     2/a   pi\
                      |1 + ------------| *sec |- - --|
                      |       2/a   pi\|      \2   4 /
                      |    sec |- - --||              
                      \        \2   4 //
$$\frac{4}{\sec^{2}{\left(\frac{a}{2} \right)}} - \frac{4}{\sec^{4}{\left(\frac{a}{2} \right)}} + \frac{4 \sec^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}\right)^{2} \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}$$ 
                                                 4/a   pi\       
                                           16*sin |- + --|       
       4/pi   a\        2/pi   a\                 \2   4 /       
- 4*sin |-- + -| + 4*sin |-- + -| + -----------------------------
        \2    2/         \2    2/                       2        
                                    /         4/a   pi\\         
                                    |    4*sin |- + --||         
                                    |          \2   4 /|     2   
                                    |1 + --------------| *cos (a)
                                    |          2       |         
                                    \       cos (a)    /
$$- 4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{2} \right)} + 4 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{2} \right)} + \frac{16 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cos^{2}{\left(a \right)}} + 1\right)^{2} \cos^{2}{\left(a \right)}}$$ 
                                     2             
                    /           /a\ \              
                  2 |      2*cot|-| |              
/         1      \  |           \2/ |     4/a   pi\
|1 + ------------| *|1 + -----------| *cot |- + --|
|       2/a   pi\|  |           2/a\|      \2   4 /
|    cot |- + --||  |    1 + cot |-||              
\        \2   4 //  \            \2//              
---------------------------------------------------
                         4
$$\frac{\left(1 + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right)^{2} \left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right)^{2} \cot^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{4}$$ 
                 4                  2                      
    /       2/a\\      /       2/a\\            2/a   pi\  
  4*|1 - tan |-||    4*|1 - tan |-||       4*tan |- + --|  
    \        \4//      \        \4//             \2   4 /  
- ---------------- + ---------------- + -------------------
                4                  2                      2
   /       2/a\\      /       2/a\\     /       2/a   pi\\ 
   |1 + tan |-||      |1 + tan |-||     |1 + tan |- + --|| 
   \        \4//      \        \4//     \        \2   4 //
$$- \frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4}} + \frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}$$ 
                  2                           
/       2/a   pi\\              2    4/a   pi\
|1 + tan |- + --|| *(1 + sin(a)) *cot |- + --|
\        \2   4 //                    \2   4 /
----------------------------------------------
                      4
$$\frac{\left(\sin{\left(a \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \cot^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{4}$$ 
   2           4/a\        2/a\
cos (a) - 4*cos |-| + 4*cos |-|
                \2/         \2/
$$- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} + \cos^{2}{\left(a \right)}$$ 
cos(a)^2 - 4*cos(a/2)^4 + 4*cos(a/2)^2
Potencias [src] 
   2         2   
cos (a) + sin (a)
-----------------
    2       2    
 cot (a)*tan (a)
$$\frac{\sin^{2}{\left(a \right)} + \cos^{2}{\left(a \right)}}{\tan^{2}{\left(a \right)} \cot^{2}{\left(a \right)}}$$ 
                              /                                2                                     2\ 
                              |/   /    3*pi\      /     3*pi\\    /     /    3*pi\      /     3*pi\\ | 
                              || I*|a - ----|    I*|-a + ----||    |   I*|a - ----|    I*|-a + ----|| | 
                            2 ||   \     2  /      \      2  /|    |     \     2  /      \      2  /| | 
 / I*(pi - a)    I*(a - pi)\  ||e               e             |    \- e             + e             / | 
-\e           + e          / *||------------- + --------------|  - -----------------------------------| 
                              \\      2               2       /                     4                 / 
--------------------------------------------------------------------------------------------------------
                                                              2                                         
                                 /   I*(pi - a)    I*(a - pi)\     2                                    
                                 \- e           + e          / *cot (a)
$$- \frac{\left(\left(\frac{e^{i \left(- a + \frac{3 \pi}{2}\right)}}{2} + \frac{e^{i \left(a - \frac{3 \pi}{2}\right)}}{2}\right)^{2} - \frac{\left(e^{i \left(- a + \frac{3 \pi}{2}\right)} - e^{i \left(a - \frac{3 \pi}{2}\right)}\right)^{2}}{4}\right) \left(e^{i \left(\pi - a\right)} + e^{i \left(a - \pi\right)}\right)^{2}}{\left(- e^{i \left(\pi - a\right)} + e^{i \left(a - \pi\right)}\right)^{2} \cot^{2}{\left(a \right)}}$$ 
-(exp(i*(pi - a)) + exp(i*(a - pi)))^2*((exp(i*(a - 3*pi/2))/2 + exp(i*(-a + 3*pi/2))/2)^2 - (-exp(i*(a - 3*pi/2)) + exp(i*(-a + 3*pi/2)))^2/4)/((-exp(i*(pi - a)) + exp(i*(a - pi)))^2*cot(a)^2)
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