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Simplificación de expresiones/ Descomposición en fracciones simples/ cot(pi/(2-a))*(-sin(a-3*pi/2)-sin(a))/((cot(a)*(cos(a)-(-1)*sin(a))))

¿Cómo vas a descomponer esta cot(pi/(2-a))(-sin(a-3pi/2)-sin(a))/((cot(a)(cos(a)-(-1)sin(a)))) expresión en fracciones?

Solución

Ha introducido [src]

   /  pi \ /     /    3*pi\         \
cot|-----|*|- sin|a - ----| - sin(a)|
   \2 - a/ \     \     2  /         /
-------------------------------------
       cot(a)*(cos(a) + sin(a))

\frac{\left(- \sin{\left(a \right)} - \sin{\left(a - \frac{3 \pi}{2} \right)}\right) \cot{\left(\frac{\pi}{2 - a} \right)}}{\left(\sin{\left(a \right)} + \cos{\left(a \right)}\right) \cot{\left(a \right)}}

(cot(pi/(2 - a))*(-sin(a - 3*pi/2) - sin(a)))/((cot(a)*(cos(a) + sin(a))))

Simplificación general [src]

   /  pi  \       
cot|------|*tan(a)
   \-2 + a/

\tan{\left(a \right)} \cot{\left(\frac{\pi}{a - 2} \right)}

cot(pi/(-2 + a))*tan(a)

Denominador común [src]

    /  pi \ 
-cot|-----| 
    \2 - a/ 
------------
   cot(a)

- \frac{\cot{\left(\frac{\pi}{2 - a} \right)}}{\cot{\left(a \right)}}

-cot(pi/(2 - a))/cot(a)

Unión de expresiones racionales [src]

/             /-3*pi + 2*a\\    /  pi \
|-sin(a) - sin|-----------||*cot|-----|
\             \     2     //    \2 - a/
---------------------------------------
        (cos(a) + sin(a))*cot(a)

\frac{\left(- \sin{\left(a \right)} - \sin{\left(\frac{2 a - 3 \pi}{2} \right)}\right) \cot{\left(\frac{\pi}{2 - a} \right)}}{\left(\sin{\left(a \right)} + \cos{\left(a \right)}\right) \cot{\left(a \right)}}

(-sin(a) - sin((-3*pi + 2*a)/2))*cot(pi/(2 - a))/((cos(a) + sin(a))*cot(a))

Denominador racional [src]

   /  pi  \
cot|------|
   \-2 + a/
-----------
   cot(a)

\frac{\cot{\left(\frac{\pi}{a - 2} \right)}}{\cot{\left(a \right)}}

cot(pi/(-2 + a))/cot(a)

Combinatoria [src]

    /  pi \ 
-cot|-----| 
    \2 - a/ 
------------
   cot(a)

- \frac{\cot{\left(\frac{\pi}{2 - a} \right)}}{\cot{\left(a \right)}}

-cot(pi/(2 - a))/cot(a)

Abrimos la expresión [src]

                  /  pi \                  /  pi \             
        cos(a)*cot|-----|               cot|-----|*sin(a)      
                  \2 - a/                  \2 - a/             
- ----------------------------- - -----------------------------
  cos(a)*cot(a) + cot(a)*sin(a)   cos(a)*cot(a) + cot(a)*sin(a)

- \frac{\sin{\left(a \right)} \cot{\left(\frac{\pi}{2 - a} \right)}}{\sin{\left(a \right)} \cot{\left(a \right)} + \cos{\left(a \right)} \cot{\left(a \right)}} - \frac{\cos{\left(a \right)} \cot{\left(\frac{\pi}{2 - a} \right)}}{\sin{\left(a \right)} \cot{\left(a \right)} + \cos{\left(a \right)} \cot{\left(a \right)}}

-cos(a)*cot(pi/(2 - a))/(cos(a)*cot(a) + cot(a)*sin(a)) - cot(pi/(2 - a))*sin(a)/(cos(a)*cot(a) + cot(a)*sin(a))

Respuesta numérica [src]

(-sin(a) - sin(a - 3*pi/2))*cot(pi/(2 - a))/((cos(a) + sin(a))*cot(a))

(-sin(a) - sin(a - 3*pi/2))*cot(pi/(2 - a))/((cos(a) + sin(a))*cot(a))

Parte trigonométrica [src]

      /       /pi    \\                        
      |    csc|-- - a||                        
  ___ |       \2     /|    /  pi  \    /    pi\
\/ 2 *|1 + -----------|*csc|------|*csc|a + --|
      \       csc(a)  /    \-2 + a/    \    4 /
-----------------------------------------------
                       /pi     pi  \           
           2*csc(a)*csc|-- - ------|           
                       \2    -2 + a/

\frac{\sqrt{2} \left(1 + \frac{\csc{\left(- a + \frac{\pi}{2} \right)}}{\csc{\left(a \right)}}\right) \csc{\left(\frac{\pi}{a - 2} \right)} \csc{\left(a + \frac{\pi}{4} \right)}}{2 \csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a - 2} \right)}}

    /  pi  \    /    pi\ 
 cos|------|*cos|a - --| 
    \-2 + a/    \    2 / 
-------------------------
          /  pi     pi  \
cos(a)*cos|- -- + ------|
          \  2    -2 + a/

\frac{\cos{\left(\frac{\pi}{a - 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{\cos{\left(a \right)} \cos{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)}}

   /  pi  \       
cot|------|*tan(a)
   \-2 + a/

\tan{\left(a \right)} \cot{\left(\frac{\pi}{a - 2} \right)}

      /           /      1   \    /a   pi\\                                   
      |           |1 + ------|*csc|- + --||                                   
  ___ |    1      \    csc(a)/    \2   4 /|    /  pi \    /    pi\    /pi    \
\/ 2 *|- ------ - ------------------------|*csc|-----|*csc|a + --|*csc|-- - a|
      |  csc(a)           /  a   pi\      |    \2 - a/    \    4 /    \2     /
      |                csc|- - + --|      |                                   
      \                   \  2   4 /      /                                   
------------------------------------------------------------------------------
                                       /pi     pi \                           
                           2*csc(a)*csc|-- - -----|                           
                                       \2    2 - a/

\frac{\sqrt{2} \left(- \frac{\left(1 + \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\csc{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}} - \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(\frac{\pi}{2 - a} \right)} \csc{\left(- a + \frac{\pi}{2} \right)} \csc{\left(a + \frac{\pi}{4} \right)}}{2 \csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{2 - a} \right)}}

          /  pi     pi  \
sec(a)*sec|- -- + ------|
          \  2    -2 + a/
-------------------------
    /  pi  \    /    pi\ 
 sec|------|*sec|a - --| 
    \-2 + a/    \    2 /

\frac{\sec{\left(a \right)} \sec{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)}}{\sec{\left(\frac{\pi}{a - 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}

   /  pi  \
cot|------|
   \-2 + a/
-----------
   cot(a)

\frac{\cot{\left(\frac{\pi}{a - 2} \right)}}{\cot{\left(a \right)}}

      /                /       /    pi\\    /a   pi\\                       
      |                |1 + cos|a - --||*cos|- + --||                       
  ___ |     /    pi\   \       \    2 //    \2   4 /|    /  pi \    /    pi\
\/ 2 *|- cos|a - --| - -----------------------------|*cos|-----|*cos|a - --|
      |     \    2 /               /a   pi\         |    \2 - a/    \    2 /
      |                         cos|- - --|         |                       
      \                            \2   4 /         /                       
----------------------------------------------------------------------------
                               /    pi\    /  pi     pi \                   
                   2*cos(a)*cos|a - --|*cos|- -- + -----|                   
                               \    4 /    \  2    2 - a/

\frac{\sqrt{2} \left(- \frac{\left(\cos{\left(a - \frac{\pi}{2} \right)} + 1\right) \cos{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cos{\left(\frac{a}{2} - \frac{\pi}{4} \right)}} - \cos{\left(a - \frac{\pi}{2} \right)}\right) \cos{\left(\frac{\pi}{2 - a} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{2 \cos{\left(a \right)} \cos{\left(- \frac{\pi}{2} + \frac{\pi}{2 - a} \right)} \cos{\left(a - \frac{\pi}{4} \right)}}

      /                       2            \
  ___ |            /a\   2*sin (a)         |
\/ 2 *|- tan(a)*tan|-| + --------- + tan(a)|
      \            \2/     cos(a)          /
--------------------------------------------
     /       /a\\    /    pi\    /  pi  \   
   2*|1 + tan|-||*sin|a + --|*tan|------|   
     \       \2//    \    4 /    \-2 + a/

\frac{\sqrt{2} \left(\frac{2 \sin^{2}{\left(a \right)}}{\cos{\left(a \right)}} - \tan{\left(\frac{a}{2} \right)} \tan{\left(a \right)} + \tan{\left(a \right)}\right)}{2 \left(\tan{\left(\frac{a}{2} \right)} + 1\right) \sin{\left(a + \frac{\pi}{4} \right)} \tan{\left(\frac{\pi}{a - 2} \right)}}

   /  pi  \    /pi    \
csc|------|*csc|-- - a|
   \-2 + a/    \2     /
-----------------------
          /pi     pi  \
csc(a)*csc|-- - ------|
          \2    -2 + a/

\frac{\csc{\left(\frac{\pi}{a - 2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)}}{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a - 2} \right)}}

  ___    2    /          (1 + sin(a))*cos(a)\    / 2*pi\
\/ 2 *sin (a)*|-sin(a) - -------------------|*sin|-----|
              |                  2/a   pi\  |    \2 - a/
              |             2*sin |- + --|  |           
              \                   \2   4 /  /           
--------------------------------------------------------
                         2/  pi \    /    pi\           
           2*sin(2*a)*sin |-----|*sin|a + --|           
                          \2 - a/    \    4 /

\frac{\sqrt{2} \left(- \frac{\left(\sin{\left(a \right)} + 1\right) \cos{\left(a \right)}}{2 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} - \sin{\left(a \right)}\right) \sin^{2}{\left(a \right)} \sin{\left(\frac{2 \pi}{2 - a} \right)}}{2 \sin{\left(2 a \right)} \sin^{2}{\left(\frac{\pi}{2 - a} \right)} \sin{\left(a + \frac{\pi}{4} \right)}}

                      /  pi \       
(-cos(a) - sin(a))*cos|-----|*sin(a)
                      \2 - a/       
------------------------------------
                            /  pi \ 
(cos(a) + sin(a))*cos(a)*sin|-----| 
                            \2 - a/

\frac{\left(- \sin{\left(a \right)} - \cos{\left(a \right)}\right) \sin{\left(a \right)} \cos{\left(\frac{\pi}{2 - a} \right)}}{\left(\sin{\left(a \right)} + \cos{\left(a \right)}\right) \sin{\left(\frac{\pi}{2 - a} \right)} \cos{\left(a \right)}}

       /                               2   \ 
   ___ |                    /a\   2*sin (a)| 
-\/ 2 *|-tan(a) + tan(a)*tan|-| - ---------| 
       \                    \2/     cos(a) / 
---------------------------------------------
      /       /a\\    /    pi\    /  pi  \   
    2*|1 + tan|-||*sin|a + --|*tan|------|   
      \       \2//    \    4 /    \-2 + a/

- \frac{\sqrt{2} \left(- \frac{2 \sin^{2}{\left(a \right)}}{\cos{\left(a \right)}} + \tan{\left(\frac{a}{2} \right)} \tan{\left(a \right)} - \tan{\left(a \right)}\right)}{2 \left(\tan{\left(\frac{a}{2} \right)} + 1\right) \sin{\left(a + \frac{\pi}{4} \right)} \tan{\left(\frac{\pi}{a - 2} \right)}}

  ___ /       2/a   pi\\ /                   /a\\       
\/ 2 *|1 + tan |- + --||*|-1 - 2*sin(a) + tan|-||*tan(a)
      \        \2   8 // \                   \2//       
--------------------------------------------------------
           /       /a\\    /  pi \    /a   pi\          
         4*|1 + tan|-||*tan|-----|*tan|- + --|          
           \       \2//    \2 - a/    \2   8 /

\frac{\sqrt{2} \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1\right) \left(- 2 \sin{\left(a \right)} + \tan{\left(\frac{a}{2} \right)} - 1\right) \tan{\left(a \right)}}{4 \left(\tan{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(\frac{\pi}{2 - a} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}

  ___ /       sin(a)  \           / 2*pi \
\/ 2 *|1 + -----------|*sin(a)*sin|------|
      |       /    pi\|           \-2 + a/
      |    sin|a + --||                   
      \       \    2 //                   
------------------------------------------
             2/  pi  \    /    pi\        
        4*sin |------|*sin|a + --|        
              \-2 + a/    \    4 /

\frac{\sqrt{2} \left(\frac{\sin{\left(a \right)}}{\sin{\left(a + \frac{\pi}{2} \right)}} + 1\right) \sin{\left(a \right)} \sin{\left(\frac{2 \pi}{a - 2} \right)}}{4 \sin^{2}{\left(\frac{\pi}{a - 2} \right)} \sin{\left(a + \frac{\pi}{4} \right)}}

    2       / 2*pi \ 
 sin (a)*sin|------| 
            \-2 + a/ 
---------------------
            2/  pi  \
sin(2*a)*sin |------|
             \-2 + a/

\frac{\sin^{2}{\left(a \right)} \sin{\left(\frac{2 \pi}{a - 2} \right)}}{\sin{\left(2 a \right)} \sin^{2}{\left(\frac{\pi}{a - 2} \right)}}

/         /a\          /a   pi\  \           
|    2*cot|-|     2*cot|- + --|  |           
|         \2/          \2   4 /  |    /  pi \
|- ----------- - ----------------|*cot|-----|
|         2/a\          2/a   pi\|    \2 - a/
|  1 + cot |-|   1 + cot |- + --||           
\          \2/           \2   4 //           
---------------------------------------------
     /        2/a\          /a\ \            
     |-1 + cot |-|     2*cot|-| |            
     |         \2/          \2/ |            
     |------------ + -----------|*cot(a)     
     |       2/a\           2/a\|            
     |1 + cot |-|    1 + cot |-||            
     \        \2/            \2//

\frac{\left(- \frac{2 \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \cot{\left(\frac{\pi}{2 - a} \right)}}{\left(\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \cot{\left(a \right)}}

      2                          / 2*pi\   
   sin (a)*(-cos(a) - sin(a))*sin|-----|   
                                 \2 - a/   
-------------------------------------------
/            /    pi\\             2/  pi \
|sin(a) + sin|a + --||*sin(2*a)*sin |-----|
\            \    2 //              \2 - a/

\frac{\left(- \sin{\left(a \right)} - \cos{\left(a \right)}\right) \sin^{2}{\left(a \right)} \sin{\left(\frac{2 \pi}{2 - a} \right)}}{\left(\sin{\left(a \right)} + \sin{\left(a + \frac{\pi}{2} \right)}\right) \sin{\left(2 a \right)} \sin^{2}{\left(\frac{\pi}{2 - a} \right)}}

/                    /    pi\\    /  pi \    /    pi\
|-cos(a - 2*pi) - cos|a - --||*cos|-----|*cos|a - --|
\                    \    2 //    \2 - a/    \    2 /
-----------------------------------------------------
   /            /    pi\\           /  pi     pi \   
   |cos(a) + cos|a - --||*cos(a)*cos|- -- + -----|   
   \            \    2 //           \  2    2 - a/

\frac{\left(- \cos{\left(a - 2 \pi \right)} - \cos{\left(a - \frac{\pi}{2} \right)}\right) \cos{\left(\frac{\pi}{2 - a} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{\left(\cos{\left(a \right)} + \cos{\left(a - \frac{\pi}{2} \right)}\right) \cos{\left(a \right)} \cos{\left(- \frac{\pi}{2} + \frac{\pi}{2 - a} \right)}}

                         /           /a\ \       
                         |      2*tan|-| |       
  ___ /       2/a   pi\\ |           \2/ |    /a\
\/ 2 *|1 + tan |- + --||*|1 + -----------|*tan|-|
      \        \2   8 // |           2/a\|    \2/
                         |    1 - tan |-||       
                         \            \2//       
-------------------------------------------------
       /       2/a\\    /  pi  \    /a   pi\     
     2*|1 + tan |-||*tan|------|*tan|- + --|     
       \        \2//    \-2 + a/    \2   8 /

\frac{\sqrt{2} \left(1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{1 - \tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1\right) \tan{\left(\frac{a}{2} \right)}}{2 \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(\frac{\pi}{a - 2} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}

                         /             /a\               \       
                         |        2*tan|-|               |       
                         |             \2/               |       
                         |  1 + -----------              |       
                         |             2/a\          /a\ |       
                         |      1 + tan |-|     2*tan|-| |       
  ___ /       2/a   pi\\ |              \2/          \2/ |       
\/ 2 *|1 + tan |- + --||*|- --------------- - -----------|*tan(a)
      \        \2   8 // |       /a   pi\            2/a\|       
                         |    tan|- + --|     1 + tan |-||       
                         \       \2   4 /             \2//       
-----------------------------------------------------------------
                          /  pi \    /a   pi\                    
                     4*tan|-----|*tan|- + --|                    
                          \2 - a/    \2   8 /

\frac{\sqrt{2} \left(- \frac{1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}}{\tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1\right) \tan{\left(a \right)}}{4 \tan{\left(\frac{\pi}{2 - a} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}

  ___ /       sec(a)  \    /    pi\    /  pi     pi  \
\/ 2 *|1 + -----------|*sec|a - --|*sec|- -- + ------|
      |       /    pi\|    \    4 /    \  2    -2 + a/
      |    sec|a - --||                               
      \       \    2 //                               
------------------------------------------------------
                   /  pi  \    /    pi\               
              2*sec|------|*sec|a - --|               
                   \-2 + a/    \    2 /

\frac{\sqrt{2} \left(\frac{\sec{\left(a \right)}}{\sec{\left(a - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)} \sec{\left(a - \frac{\pi}{4} \right)}}{2 \sec{\left(\frac{\pi}{a - 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}

                         /           /a\  \                   
                         |      2*cot|-|  |                   
  ___ /       2/a   pi\\ |           \2/  |    /a\    /  pi  \
\/ 2 *|1 + cot |- + --||*|1 + ------------|*cot|-|*cot|------|
      \        \2   8 // |            2/a\|    \2/    \-2 + a/
                         |    -1 + cot |-||                   
                         \             \2//                   
--------------------------------------------------------------
                   /       2/a\\    /a   pi\                  
                 2*|1 + cot |-||*cot|- + --|                  
                   \        \2//    \2   8 /

\frac{\sqrt{2} \left(1 + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} - 1}\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1\right) \cot{\left(\frac{a}{2} \right)} \cot{\left(\frac{\pi}{a - 2} \right)}}{2 \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \cot{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}

    /  pi \       
-cot|-----|*tan(a)
    \2 - a/

- \tan{\left(a \right)} \cot{\left(\frac{\pi}{2 - a} \right)}

      /       /    pi\\                        
      |    cos|a - --||                        
  ___ |       \    2 /|    /  pi  \    /    pi\
\/ 2 *|1 + -----------|*cos|------|*cos|a - --|
      \       cos(a)  /    \-2 + a/    \    2 /
-----------------------------------------------
             /    pi\    /  pi     pi  \       
        2*cos|a - --|*cos|- -- + ------|       
             \    4 /    \  2    -2 + a/

\frac{\sqrt{2} \left(1 + \frac{\cos{\left(a - \frac{\pi}{2} \right)}}{\cos{\left(a \right)}}\right) \cos{\left(\frac{\pi}{a - 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{2 \cos{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)} \cos{\left(a - \frac{\pi}{4} \right)}}

/        1              1     \           /  pi     pi \
|- ------------- - -----------|*sec(a)*sec|- -- + -----|
|  sec(a - 2*pi)      /    pi\|           \  2    2 - a/
|                  sec|a - --||                         
\                     \    2 //                         
--------------------------------------------------------
     /  1           1     \    /  pi \    /    pi\      
     |------ + -----------|*sec|-----|*sec|a - --|      
     |sec(a)      /    pi\|    \2 - a/    \    2 /      
     |         sec|a - --||                             
     \            \    2 //

\frac{\left(- \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(a - 2 \pi \right)}}\right) \sec{\left(a \right)} \sec{\left(- \frac{\pi}{2} + \frac{\pi}{2 - a} \right)}}{\left(\frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(a \right)}}\right) \sec{\left(\frac{\pi}{2 - a} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}

  ___    2/a\                 /a\    /  pi  \    /a   pi\
\/ 2 *sin |-|*(1 + tan(a))*cot|-|*cot|------|*tan|- + --|
          \2/                 \2/    \-2 + a/    \2   8 /
---------------------------------------------------------
                           2/a   pi\                     
                      2*sin |- + --|                     
                            \2   8 /

\frac{\sqrt{2} \left(\tan{\left(a \right)} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{8} \right)} \cot{\left(\frac{a}{2} \right)} \cot{\left(\frac{\pi}{a - 2} \right)}}{2 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}

  /    1        1   \    /  pi \    /pi    \ 
  |- ------ - ------|*csc|-----|*csc|-- - a| 
  \  csc(a)   sec(a)/    \2 - a/    \2     / 
---------------------------------------------
/  1           1     \           /pi     pi \
|------ + -----------|*csc(a)*csc|-- - -----|
|csc(a)      /pi    \|           \2    2 - a/
|         csc|-- - a||                       
\            \2     //

\frac{\left(- \frac{1}{\sec{\left(a \right)}} - \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(\frac{\pi}{2 - a} \right)} \csc{\left(- a + \frac{\pi}{2} \right)}}{\left(\frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{2 - a} \right)}}

      /                /         1     \    /a   pi\\                                     
      |                |1 + -----------|*sec|- - --||                                     
      |                |       /    pi\|    \2   4 /|                                     
      |                |    sec|a - --||            |                                     
  ___ |       1        \       \    2 //            |           /    pi\    /  pi     pi \
\/ 2 *|- ----------- - -----------------------------|*sec(a)*sec|a - --|*sec|- -- + -----|
      |     /    pi\               /a   pi\         |           \    4 /    \  2    2 - a/
      |  sec|a - --|            sec|- + --|         |                                     
      \     \    2 /               \2   4 /         /                                     
------------------------------------------------------------------------------------------
                                      /  pi \    /    pi\                                 
                                 2*sec|-----|*sec|a - --|                                 
                                      \2 - a/    \    2 /

\frac{\sqrt{2} \left(- \frac{\left(1 + \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right) \sec{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\sec{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} - \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right) \sec{\left(a \right)} \sec{\left(- \frac{\pi}{2} + \frac{\pi}{2 - a} \right)} \sec{\left(a - \frac{\pi}{4} \right)}}{2 \sec{\left(\frac{\pi}{2 - a} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}

/    1           1     \    /  pi \       
|- ------ - -----------|*csc|-----|*sec(a)
|  csc(a)      /pi    \|    \2 - a/       
|           csc|-- - a||                  
\              \2     //                  
------------------------------------------
   /  1        1   \           /  pi \    
   |------ + ------|*csc(a)*sec|-----|    
   \csc(a)   sec(a)/           \2 - a/

\frac{\left(- \frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(\frac{\pi}{2 - a} \right)} \sec{\left(a \right)}}{\left(\frac{1}{\sec{\left(a \right)}} + \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(a \right)} \sec{\left(\frac{\pi}{2 - a} \right)}}

/    1        1   \    /  pi \       
|- ------ - ------|*csc|-----|*sec(a)
\  csc(a)   sec(a)/    \2 - a/       
-------------------------------------
 /  1        1   \           /  pi \ 
 |------ + ------|*csc(a)*sec|-----| 
 \csc(a)   sec(a)/           \2 - a/

\frac{\left(- \frac{1}{\sec{\left(a \right)}} - \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(\frac{\pi}{2 - a} \right)} \sec{\left(a \right)}}{\left(\frac{1}{\sec{\left(a \right)}} + \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(a \right)} \sec{\left(\frac{\pi}{2 - a} \right)}}

                         /  /           /a\ \                      /a\ \           
                         |  |      2*cot|-| |                 2*cot|-| |           
  ___ /       2/a   pi\\ |  |           \2/ |    /a   pi\          \2/ |    /  pi \
\/ 2 *|1 + cot |- + --||*|- |1 + -----------|*cot|- + --| - -----------|*cot|-----|
      \        \2   8 // |  |           2/a\|    \2   4 /          2/a\|    \2 - a/
                         |  |    1 + cot |-||               1 + cot |-||           
                         \  \            \2//                       \2//           
-----------------------------------------------------------------------------------
                                            /a   pi\                               
                                4*cot(a)*cot|- + --|                               
                                            \2   8 /

\frac{\sqrt{2} \left(- \left(1 + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1\right) \cot{\left(\frac{\pi}{2 - a} \right)}}{4 \cot{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}

  ___ /                          /a   pi\\    /  pi \       
\/ 2 *|-sin(a) - (1 + sin(a))*cot|- + --||*cot|-----|*tan(a)
      \                          \2   4 //    \2 - a/       
------------------------------------------------------------
                            /    pi\                        
                       2*sin|a + --|                        
                            \    4 /

\frac{\sqrt{2} \left(- \left(\sin{\left(a \right)} + 1\right) \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - \sin{\left(a \right)}\right) \tan{\left(a \right)} \cot{\left(\frac{\pi}{2 - a} \right)}}{2 \sin{\left(a + \frac{\pi}{4} \right)}}

  ___ /    sin(a)\       
\/ 2 *|1 + ------|*sin(a)
      \    cos(a)/       
-------------------------
     /    pi\    /  pi  \
2*sin|a + --|*tan|------|
     \    4 /    \-2 + a/

\frac{\sqrt{2} \left(\frac{\sin{\left(a \right)}}{\cos{\left(a \right)}} + 1\right) \sin{\left(a \right)}}{2 \sin{\left(a + \frac{\pi}{4} \right)} \tan{\left(\frac{\pi}{a - 2} \right)}}

   tan(a)  
-----------
   /  pi  \
tan|------|
   \-2 + a/

\frac{\tan{\left(a \right)}}{\tan{\left(\frac{\pi}{a - 2} \right)}}

/         /a\          /a   pi\  \       
|    2*tan|-|     2*tan|- + --|  |       
|         \2/          \2   4 /  |       
|- ----------- - ----------------|*tan(a)
|         2/a\          2/a   pi\|       
|  1 + tan |-|   1 + tan |- + --||       
\          \2/           \2   4 //       
-----------------------------------------
  /       2/a\          /a\ \            
  |1 - tan |-|     2*tan|-| |            
  |        \2/          \2/ |    /  pi \ 
  |----------- + -----------|*tan|-----| 
  |       2/a\          2/a\|    \2 - a/ 
  |1 + tan |-|   1 + tan |-||            
  \        \2/           \2//

\frac{\left(- \frac{2 \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \tan{\left(a \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \tan{\left(\frac{\pi}{2 - a} \right)}}

  ___    2/a\ /       2/a   pi\\                 /a\
\/ 2 *cos |-|*|1 + tan |- + --||*(1 + tan(a))*tan|-|
          \2/ \        \2   8 //                 \2/
----------------------------------------------------
                  /  pi  \    /a   pi\              
             2*tan|------|*tan|- + --|              
                  \-2 + a/    \2   8 /

\frac{\sqrt{2} \left(\tan{\left(a \right)} + 1\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1\right) \cos^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{a}{2} \right)}}{2 \tan{\left(\frac{\pi}{a - 2} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}

   2    /             /    pi\\    / 2*pi\
sin (a)*|-sin(a) - sin|a + --||*sin|-----|
        \             \    2 //    \2 - a/
------------------------------------------
                                2/  pi \  
  (cos(a) + sin(a))*sin(2*a)*sin |-----|  
                                 \2 - a/

\frac{\left(- \sin{\left(a \right)} - \sin{\left(a + \frac{\pi}{2} \right)}\right) \sin^{2}{\left(a \right)} \sin{\left(\frac{2 \pi}{2 - a} \right)}}{\left(\sin{\left(a \right)} + \cos{\left(a \right)}\right) \sin{\left(2 a \right)} \sin^{2}{\left(\frac{\pi}{2 - a} \right)}}

  ___ /                          /a   pi\\    /  pi \           /a   pi\
\/ 2 *|-sin(a) - (1 + sin(a))*cot|- + --||*cot|-----|*tan(a)*tan|- + --|
      \                          \2   4 //    \2 - a/           \2   8 /
------------------------------------------------------------------------
                                  2/a   pi\                             
                             4*sin |- + --|                             
                                   \2   8 /

\frac{\sqrt{2} \left(- \left(\sin{\left(a \right)} + 1\right) \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - \sin{\left(a \right)}\right) \tan{\left(a \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{8} \right)} \cot{\left(\frac{\pi}{2 - a} \right)}}{4 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}

sqrt(2)*(-sin(a) - (1 + sin(a))*cot(a/2 + pi/4))*cot(pi/(2 - a))*tan(a)*tan(a/2 + pi/8)/(4*sin(a/2 + pi/8)^2)

Potencias [src]

/  /     /     3*pi\      /    3*pi\\                     \           
|  |   I*|-a + ----|    I*|a - ----||                     |           
|  |     \      2  /      \     2  /|     /   -I*a    I*a\|           
|I*\- e              + e            /   I*\- e     + e   /|    /  pi \
|------------------------------------ + ------------------|*cot|-----|
\                 2                             2         /    \2 - a/
----------------------------------------------------------------------
              / I*a    -I*a     /   -I*a    I*a\\                     
              |e      e       I*\- e     + e   /|                     
              |---- + ----- - ------------------|*cot(a)              
              \ 2       2             2         /

\frac{\left(\frac{i \left(e^{i a} - e^{- i a}\right)}{2} + \frac{i \left(- e^{i \left(- a + \frac{3 \pi}{2}\right)} + e^{i \left(a - \frac{3 \pi}{2}\right)}\right)}{2}\right) \cot{\left(\frac{\pi}{2 - a} \right)}}{\left(- \frac{i \left(e^{i a} - e^{- i a}\right)}{2} + \frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right) \cot{\left(a \right)}}

                      /  pi \
(-cos(a) - sin(a))*cot|-----|
                      \2 - a/
-----------------------------
   (cos(a) + sin(a))*cot(a)

\frac{\left(- \sin{\left(a \right)} - \cos{\left(a \right)}\right) \cot{\left(\frac{\pi}{2 - a} \right)}}{\left(\sin{\left(a \right)} + \cos{\left(a \right)}\right) \cot{\left(a \right)}}

    /  pi \ 
-cot|-----| 
    \2 - a/ 
------------
   cot(a)

- \frac{\cot{\left(\frac{\pi}{2 - a} \right)}}{\cot{\left(a \right)}}

-cot(pi/(2 - a))/cot(a)

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¿Cómo vas a descomponer esta cot(pi/(2-a))(-sin(a-3pi/2)-sin(a))/((cot(a)(cos(a)-(-1)sin(a)))) expresión en fracciones?

Solución

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¿Cómo vas a descomponer esta cot(pi/(2-a))*(-sin(a-3*pi/2)-sin(a))/((cot(a)*(cos(a)-(-1)*sin(a)))) expresión en fracciones?

Solución

¿Cómo vas a descomponer esta cot(pi/(2-a))(-sin(a-3pi/2)-sin(a))/((cot(a)(cos(a)-(-1)sin(a)))) expresión en fracciones?