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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   /pi    \ /    /    3*pi\\                          
sin|-- + a|*|-cot|a - ----||                          
   \2     / \    \     2  //      /    3*pi\          
---------------------------- - tan|a - ----|*(-cos(a))
                  2               \     2  /          
         (-sin(a))
−−cos⁡(a)tan⁡(a−3π2)+sin⁡(a+π2)(−cot⁡(a−3π2))(−sin⁡(a))2- - \cos{\left(a \right)} \tan{\left(a - \frac{3 \pi}{2} \right)} + \frac{\sin{\left(a + \frac{\pi}{2} \right)} \left(- \cot{\left(a - \frac{3 \pi}{2} \right)}\right)}{\left(- \sin{\left(a \right)}\right)^{2}} 
(sin(pi/2 + a)*(-cot(a - 3*pi/2)))/(-sin(a))^2 - tan(a - 3*pi/2)*(-cos(a))
Simplificación general [src] 
sin(a)
sin⁡(a)\sin{\left(a \right)} 
sin(a)
Denominador racional [src] 
   /    pi\             2                 
sin|a + --|*tan(a) - sin (a)*cos(a)*cot(a)
   \    2 /                               
------------------------------------------
                    2                     
                 sin (a)
−sin⁡2(a)cos⁡(a)cot⁡(a)+sin⁡(a+π2)tan⁡(a)sin⁡2(a)\frac{- \sin^{2}{\left(a \right)} \cos{\left(a \right)} \cot{\left(a \right)} + \sin{\left(a + \frac{\pi}{2} \right)} \tan{\left(a \right)}}{\sin^{2}{\left(a \right)}} 
(sin(a + pi/2)*tan(a) - sin(a)^2*cos(a)*cot(a))/sin(a)^2
Denominador común [src] 
                 cos(a)*tan(a)
-cos(a)*cot(a) + -------------
                       2      
                    sin (a)
−cos⁡(a)cot⁡(a)+cos⁡(a)tan⁡(a)sin⁡2(a)- \cos{\left(a \right)} \cot{\left(a \right)} + \frac{\cos{\left(a \right)} \tan{\left(a \right)}}{\sin^{2}{\left(a \right)}} 
-cos(a)*cot(a) + cos(a)*tan(a)/sin(a)^2
Potencias [src] 
    /     /    3*pi\      /     3*pi\\                                                             
    |   I*|a - ----|    I*|-a + ----|| /   I*a    -I*a\       /     /     pi\      /    pi\\       
    |     \     2  /      \      2  /| |  e      e    |       |   I*|-a - --|    I*|a + --||       
  I*\- e             + e             /*|- ---- - -----|       |     \     2 /      \    2 /|       
                                       \   2       2  /   2*I*\- e            + e          /*tan(a)
- ----------------------------------------------------- + -----------------------------------------
                 /    3*pi\      /     3*pi\                                          2            
               I*|a - ----|    I*|-a + ----|                          /   -I*a    I*a\             
                 \     2  /      \      2  /                          \- e     + e   /             
              e             + e
−i(−eia2−e−ia2)(ei(−a+3π2)−ei(a−3π2))ei(−a+3π2)+ei(a−3π2)+2i(−ei(−a−π2)+ei(a+π2))tan⁡(a)(eia−e−ia)2- \frac{i \left(- \frac{e^{i a}}{2} - \frac{e^{- i a}}{2}\right) \left(e^{i \left(- a + \frac{3 \pi}{2}\right)} - e^{i \left(a - \frac{3 \pi}{2}\right)}\right)}{e^{i \left(- a + \frac{3 \pi}{2}\right)} + e^{i \left(a - \frac{3 \pi}{2}\right)}} + \frac{2 i \left(- e^{i \left(- a - \frac{\pi}{2}\right)} + e^{i \left(a + \frac{\pi}{2}\right)}\right) \tan{\left(a \right)}}{\left(e^{i a} - e^{- i a}\right)^{2}} 
                 cos(a)*tan(a)
-cos(a)*cot(a) + -------------
                       2      
                    sin (a)
−cos⁡(a)cot⁡(a)+cos⁡(a)tan⁡(a)sin⁡2(a)- \cos{\left(a \right)} \cot{\left(a \right)} + \frac{\cos{\left(a \right)} \tan{\left(a \right)}}{\sin^{2}{\left(a \right)}} 
-cos(a)*cot(a) + cos(a)*tan(a)/sin(a)^2
Unión de expresiones racionales [src] 
     /-3*pi + 2*a\    /pi + 2*a\      2              /-3*pi + 2*a\
- cot|-----------|*sin|--------| + sin (a)*cos(a)*tan|-----------|
     \     2     /    \   2    /                     \     2     /
------------------------------------------------------------------
                                2                                 
                             sin (a)
sin⁡2(a)cos⁡(a)tan⁡(2a−3π2)−sin⁡(2a+π2)cot⁡(2a−3π2)sin⁡2(a)\frac{\sin^{2}{\left(a \right)} \cos{\left(a \right)} \tan{\left(\frac{2 a - 3 \pi}{2} \right)} - \sin{\left(\frac{2 a + \pi}{2} \right)} \cot{\left(\frac{2 a - 3 \pi}{2} \right)}}{\sin^{2}{\left(a \right)}} 
(-cot((-3*pi + 2*a)/2)*sin((pi + 2*a)/2) + sin(a)^2*cos(a)*tan((-3*pi + 2*a)/2))/sin(a)^2
Abrimos la expresión [src] 
                               /    3*pi\    /pi    \
                            cot|a - ----|*sin|-- + a|
     /    3*pi\                \     2  /    \2     /
- tan|a - ----|*(-cos(a)) - -------------------------
     \     2  /                         2            
                                     sin (a)
−−cos⁡(a)tan⁡(a−3π2)−sin⁡(a+π2)cot⁡(a−3π2)sin⁡2(a)- - \cos{\left(a \right)} \tan{\left(a - \frac{3 \pi}{2} \right)} - \frac{\sin{\left(a + \frac{\pi}{2} \right)} \cot{\left(a - \frac{3 \pi}{2} \right)}}{\sin^{2}{\left(a \right)}} 
                 cos(a)*tan(a)
-cos(a)*cot(a) + -------------
                       2      
                    sin (a)
−cos⁡(a)cot⁡(a)+cos⁡(a)tan⁡(a)sin⁡2(a)- \cos{\left(a \right)} \cot{\left(a \right)} + \frac{\cos{\left(a \right)} \tan{\left(a \right)}}{\sin^{2}{\left(a \right)}} 
-cos(a)*cot(a) + cos(a)*tan(a)/sin(a)^2
Combinatoria [src] 
 /             2          \        
-\-tan(a) + sin (a)*cot(a)/*cos(a) 
-----------------------------------
                 2                 
              sin (a)
−(sin⁡2(a)cot⁡(a)−tan⁡(a))cos⁡(a)sin⁡2(a)- \frac{\left(\sin^{2}{\left(a \right)} \cot{\left(a \right)} - \tan{\left(a \right)}\right) \cos{\left(a \right)}}{\sin^{2}{\left(a \right)}} 
-(-tan(a) + sin(a)^2*cot(a))*cos(a)/sin(a)^2
Compilar la expresión [src] 
                          /    3*pi\    /pi    \
                       cot|a - ----|*sin|-- + a|
          /    3*pi\      \     2  /    \2     /
cos(a)*tan|a - ----| - -------------------------
          \     2  /               2            
                                sin (a)
cos⁡(a)tan⁡(a−3π2)−sin⁡(a+π2)cot⁡(a−3π2)sin⁡2(a)\cos{\left(a \right)} \tan{\left(a - \frac{3 \pi}{2} \right)} - \frac{\sin{\left(a + \frac{\pi}{2} \right)} \cot{\left(a - \frac{3 \pi}{2} \right)}}{\sin^{2}{\left(a \right)}} 
cos(a)*tan(a - 3*pi/2) - cot(a - 3*pi/2)*sin(pi/2 + a)/sin(a)^2
Parte trigonométrica [src] 
sin(a)
sin⁡(a)\sin{\left(a \right)} 
                                           2                
  /       2/a\\               /       2/a\\     /a   pi\    
  |1 - tan |-||*cot(a)        |1 + tan |-|| *tan|- + --|    
  \        \2//               \        \2//     \2   4 /    
- -------------------- + -----------------------------------
             2/a\          /       2/a   pi\\           2/a\
      1 + tan |-|        2*|1 + tan |- + --||*cot(a)*tan |-|
              \2/          \        \2   4 //            \2/
−(1−tan⁡2(a2))cot⁡(a)tan⁡2(a2)+1+(tan⁡2(a2)+1)2tan⁡(a2+π4)2(tan⁡2(a2+π4)+1)tan⁡2(a2)cot⁡(a)- \frac{\left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \cot{\left(a \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{2 \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \tan^{2}{\left(\frac{a}{2} \right)} \cot{\left(a \right)}} 
     /    pi\              
  sec|a - --|              
     \    2 /      /    pi\
- ----------- + sec|a - --|
       2           \    2 /
    sec (a)
sec⁡(a−π2)−sec⁡(a−π2)sec⁡2(a)\sec{\left(a - \frac{\pi}{2} \right)} - \frac{\sec{\left(a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)}} 
                  /        1    \       
                  |1 - ---------|*tan(a)
           2/a\   |         2/a\|       
  1 - 2*sin |-|   |    2*cos |-||       
            \2/   \          \2//       
- ------------- + ----------------------
      tan(a)                 2/a\       
                        2*sin |-|       
                              \2/
−1−2sin⁡2(a2)tan⁡(a)+(1−12cos⁡2(a2))tan⁡(a)2sin⁡2(a2)- \frac{1 - 2 \sin^{2}{\left(\frac{a}{2} \right)}}{\tan{\left(a \right)}} + \frac{\left(1 - \frac{1}{2 \cos^{2}{\left(\frac{a}{2} \right)}}\right) \tan{\left(a \right)}}{2 \sin^{2}{\left(\frac{a}{2} \right)}} 
  /         2/a   pi\\          /       /    pi\\    /    pi\    /a   pi\
  |1 - 2*cos |- - --||*cos(a)   |1 + cos|a - --||*cos|a - --|*cos|- + --|
  \          \2   2 //          \       \    2 //    \    2 /    \2   4 /
- --------------------------- + -----------------------------------------
             /    pi\                       2/a\    2/a   pi\    /a   pi\
          cos|a - --|           4*cos(a)*cos |-|*cos |- - --|*cos|- - --|
             \    2 /                        \2/     \2   2 /    \2   4 /
−(1−2cos⁡2(a2−π2))cos⁡(a)cos⁡(a−π2)+(cos⁡(a−π2)+1)cos⁡(a2+π4)cos⁡(a−π2)4cos⁡2(a2)cos⁡(a)cos⁡2(a2−π2)cos⁡(a2−π4)- \frac{\left(1 - 2 \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}\right) \cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} + \frac{\left(\cos{\left(a - \frac{\pi}{2} \right)} + 1\right) \cos{\left(\frac{a}{2} + \frac{\pi}{4} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{4 \cos^{2}{\left(\frac{a}{2} \right)} \cos{\left(a \right)} \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{4} \right)}} 
  /       2   \                  /       2/pi   a\\            
  |1 - -------|*csc(a)           |    csc |-- - -||            
  |       2/a\|             2/a\ |        \2    2/|    /pi    \
  |    csc |-||          csc |-|*|1 - ------------|*csc|-- - a|
  \        \2//              \2/ \         2      /    \2     /
- -------------------- + --------------------------------------
         /pi    \                       2*csc(a)               
      csc|-- - a|                                              
         \2     /
−(1−2csc⁡2(a2))csc⁡(a)csc⁡(−a+π2)+(1−csc⁡2(−a2+π2)2)csc⁡2(a2)csc⁡(−a+π2)2csc⁡(a)- \frac{\left(1 - \frac{2}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{\left(1 - \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{2}\right) \csc^{2}{\left(\frac{a}{2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)}}{2 \csc{\left(a \right)}} 
  1                /    3*pi\
------ + cos(a)*tan|a - ----|
sin(a)             \     2  /
cos⁡(a)tan⁡(a−3π2)+1sin⁡(a)\cos{\left(a \right)} \tan{\left(a - \frac{3 \pi}{2} \right)} + \frac{1}{\sin{\left(a \right)}} 
                                               /           /a\ \            
                                             4 |      2*cot|-| |            
                                /       2/a\\  |           \2/ |    /a   pi\
                                |1 + cot |-|| *|1 + -----------|*cot|- + --|
  /           2/a\   \          \        \4//  |           2/a\|    \2   4 /
  |      8*cot |-|   |                         |    1 + cot |-||            
  |            \4/   |                         \            \2//            
- |1 - --------------|*cot(a) + --------------------------------------------
  |                 2|                                2/a\    4/a\          
  |    /       2/a\\ |                   64*cot(a)*cot |-|*cot |-|          
  |    |1 + cot |-|| |                                 \2/     \4/          
  \    \        \4// /
−(1−8cot⁡2(a4)(cot⁡2(a4)+1)2)cot⁡(a)+(1+2cot⁡(a2)cot⁡2(a2)+1)(cot⁡2(a4)+1)4cot⁡(a2+π4)64cot⁡4(a4)cot⁡2(a2)cot⁡(a)- \left(1 - \frac{8 \cot^{2}{\left(\frac{a}{4} \right)}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}\right) \cot{\left(a \right)} + \frac{\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}{4} \right)} + 1\right)^{4} \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{64 \cot^{4}{\left(\frac{a}{4} \right)} \cot^{2}{\left(\frac{a}{2} \right)} \cot{\left(a \right)}} 
                    2/a\    4/a\                 /a   pi\       
                 tan |-|*tan |-|*(1 + sin(a))*cot|- + --|*tan(a)
                     \2/     \4/                 \2   4 /       
-cos(a)*cot(a) + -----------------------------------------------
                                          8/a\                  
                                    64*sin |-|                  
                                           \4/
(sin⁡(a)+1)tan⁡4(a4)tan⁡2(a2)tan⁡(a)cot⁡(a2+π4)64sin⁡8(a4)−cos⁡(a)cot⁡(a)\frac{\left(\sin{\left(a \right)} + 1\right) \tan^{4}{\left(\frac{a}{4} \right)} \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{64 \sin^{8}{\left(\frac{a}{4} \right)}} - \cos{\left(a \right)} \cot{\left(a \right)} 
                           /pi    \
                 csc(a)*csc|-- - a|
     csc(a)                \2     /
- ------------ + ------------------
     2/pi    \         sec(a)      
  csc |-- - a|                     
      \2     /
csc⁡(a)csc⁡(−a+π2)sec⁡(a)−csc⁡(a)csc⁡2(−a+π2)\frac{\csc{\left(a \right)} \csc{\left(- a + \frac{\pi}{2} \right)}}{\sec{\left(a \right)}} - \frac{\csc{\left(a \right)}}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} 
             2/a\                                                     
        8*tan |-|                             /           /a\ \       
              \4/                   4         |      2*tan|-| |       
  1 - --------------   /       2/a\\     2/a\ |           \2/ |       
                   2   |1 + tan |-|| *tan |-|*|1 + -----------|*tan(a)
      /       2/a\\    \        \4//      \2/ |           2/a\|       
      |1 + tan |-||                           |    1 + tan |-||       
      \        \4//                           \            \2//       
- ------------------ + -----------------------------------------------
        tan(a)                            4/a\    /a   pi\            
                                    64*tan |-|*tan|- + --|            
                                           \4/    \2   4 /
−1−8tan⁡2(a4)(tan⁡2(a4)+1)2tan⁡(a)+(1+2tan⁡(a2)tan⁡2(a2)+1)(tan⁡2(a4)+1)4tan⁡2(a2)tan⁡(a)64tan⁡4(a4)tan⁡(a2+π4)- \frac{1 - \frac{8 \tan^{2}{\left(\frac{a}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}}{\tan{\left(a \right)}} + \frac{\left(1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4} \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(a \right)}}{64 \tan^{4}{\left(\frac{a}{4} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} 
  cos(a)*cos(a - 2*pi)         cos(a)*sin(a)       
- -------------------- + --------------------------
         sin(a)                           2/    pi\
                         cos(a - 2*pi)*cos |a - --|
                                           \    2 /
sin⁡(a)cos⁡(a)cos⁡(a−2π)cos⁡2(a−π2)−cos⁡(a)cos⁡(a−2π)sin⁡(a)\frac{\sin{\left(a \right)} \cos{\left(a \right)}}{\cos{\left(a - 2 \pi \right)} \cos^{2}{\left(a - \frac{\pi}{2} \right)}} - \frac{\cos{\left(a \right)} \cos{\left(a - 2 \pi \right)}}{\sin{\left(a \right)}} 
                                2    /          1       \
                             sin (a)*|1 - --------------|
  /         2/a\\                    |         2/pi   a\|
  |1 - 2*sin |-||*sin(2*a)           |    2*sin |-- + -||
  \          \2//                    \          \2    2//
- ------------------------ + ----------------------------
              2                       2/a\               
         2*sin (a)                 sin |-|*sin(2*a)      
                                       \2/
−(1−2sin⁡2(a2))sin⁡(2a)2sin⁡2(a)+(1−12sin⁡2(a2+π2))sin⁡2(a)sin⁡2(a2)sin⁡(2a)- \frac{\left(1 - 2 \sin^{2}{\left(\frac{a}{2} \right)}\right) \sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)}} + \frac{\left(1 - \frac{1}{2 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{2} \right)}}\right) \sin^{2}{\left(a \right)}}{\sin^{2}{\left(\frac{a}{2} \right)} \sin{\left(2 a \right)}} 
   /    pi\              
cos|a - --|        2     
   \    2 /     cos (a)  
----------- - -----------
     2           /    pi\
  sin (a)     cos|a - --|
                 \    2 /
−cos⁡2(a)cos⁡(a−π2)+cos⁡(a−π2)sin⁡2(a)- \frac{\cos^{2}{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} + \frac{\cos{\left(a - \frac{\pi}{2} \right)}}{\sin^{2}{\left(a \right)}} 
                                      2                   
              2/a\       /       2/a\\     /a   pi\       
      -1 + cot |-|       |1 + cot |-|| *cot|- + --|*tan(a)
               \2/       \        \2//     \2   4 /       
- -------------------- + ---------------------------------
  /       2/a\\               /       2/a   pi\\    2/a\  
  |1 + cot |-||*tan(a)      2*|1 + cot |- + --||*cot |-|  
  \        \2//               \        \2   4 //     \2/
−cot⁡2(a2)−1(cot⁡2(a2)+1)tan⁡(a)+(cot⁡2(a2)+1)2tan⁡(a)cot⁡(a2+π4)2(cot⁡2(a2+π4)+1)cot⁡2(a2)- \frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(a \right)}} + \frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{2 \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \cot^{2}{\left(\frac{a}{2} \right)}} 
       /a\ 
  2*cot|-| 
       \2/ 
-----------
       2/a\
1 + cot |-|
        \2/
2cot⁡(a2)cot⁡2(a2)+1\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} 
                             2/    pi\       
                        2*sin |a + --|*cos(a)
       sin(2*a)               \    2 /       
--------------------- - ---------------------
     2       /    pi\          sin(2*a)      
2*sin (a)*sin|a + --|                        
             \    2 /
−2sin⁡2(a+π2)cos⁡(a)sin⁡(2a)+sin⁡(2a)2sin⁡2(a)sin⁡(a+π2)- \frac{2 \sin^{2}{\left(a + \frac{\pi}{2} \right)} \cos{\left(a \right)}}{\sin{\left(2 a \right)}} + \frac{\sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)} \sin{\left(a + \frac{\pi}{2} \right)}} 
                                /        1    \    /    pi\
                                |1 - ---------|*cos|a - --|
  /         2/a   pi\\          |         2/a\|    \    2 /
  |1 - 2*cos |- - --||*cos(a)   |    2*cos |-||            
  \          \2   2 //          \          \2//            
- --------------------------- + ---------------------------
             /    pi\                          2/a   pi\   
          cos|a - --|              2*cos(a)*cos |- - --|   
             \    2 /                           \2   2 /
(1−12cos⁡2(a2))cos⁡(a−π2)2cos⁡(a)cos⁡2(a2−π2)−(1−2cos⁡2(a2−π2))cos⁡(a)cos⁡(a−π2)\frac{\left(1 - \frac{1}{2 \cos^{2}{\left(\frac{a}{2} \right)}}\right) \cos{\left(a - \frac{\pi}{2} \right)}}{2 \cos{\left(a \right)} \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - \frac{\left(1 - 2 \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}\right) \cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} 
                        2       /    pi\
                   2*cos (a)*sin|a + --|
    sin(2*a)                    \    2 /
---------------- - ---------------------
            2             sin(2*a)      
2*cos(a)*sin (a)
−2sin⁡(a+π2)cos⁡2(a)sin⁡(2a)+sin⁡(2a)2sin⁡2(a)cos⁡(a)- \frac{2 \sin{\left(a + \frac{\pi}{2} \right)} \cos^{2}{\left(a \right)}}{\sin{\left(2 a \right)}} + \frac{\sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)} \cos{\left(a \right)}} 
   csc(a)         
- ------- + csc(a)
     2            
  sec (a)
csc⁡(a)−csc⁡(a)sec⁡2(a)\csc{\left(a \right)} - \frac{\csc{\left(a \right)}}{\sec^{2}{\left(a \right)}} 
  1   
------
csc(a)
1csc⁡(a)\frac{1}{\csc{\left(a \right)}} 
                                  /   2            \
                     /       /a\\ |sin (a)         |
                   2*|1 - tan|-||*|------- + tan(a)|
     2               \       \2// \ cos(a)         /
- cos (a)*csc(a) + ---------------------------------
                                     /       /a\\   
                      (1 - cos(2*a))*|1 + tan|-||   
                                     \       \2//
−cos⁡2(a)csc⁡(a)+2(1−tan⁡(a2))(sin⁡2(a)cos⁡(a)+tan⁡(a))(1−cos⁡(2a))(tan⁡(a2)+1)- \cos^{2}{\left(a \right)} \csc{\left(a \right)} + \frac{2 \left(1 - \tan{\left(\frac{a}{2} \right)}\right) \left(\frac{\sin^{2}{\left(a \right)}}{\cos{\left(a \right)}} + \tan{\left(a \right)}\right)}{\left(1 - \cos{\left(2 a \right)}\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)} 
                                      2                   
             2/a\        /       2/a\\            /a   pi\
      1 - tan |-|        |1 + tan |-|| *tan(a)*tan|- + --|
              \2/        \        \2//            \2   4 /
- -------------------- + ---------------------------------
  /       2/a\\               /       2/a   pi\\    2/a\  
  |1 + tan |-||*tan(a)      2*|1 + tan |- + --||*tan |-|  
  \        \2//               \        \2   4 //     \2/
−1−tan⁡2(a2)(tan⁡2(a2)+1)tan⁡(a)+(tan⁡2(a2)+1)2tan⁡(a)tan⁡(a2+π4)2(tan⁡2(a2+π4)+1)tan⁡2(a2)- \frac{1 - \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(a \right)}} + \frac{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan{\left(a \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{2 \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \tan^{2}{\left(\frac{a}{2} \right)}} 
                                            2                
  /        2/a\\               /       2/a\\     /a   pi\    
  |-1 + cot |-||*cot(a)        |1 + cot |-|| *cot|- + --|    
  \         \2//               \        \2//     \2   4 /    
- --------------------- + -----------------------------------
              2/a\          /       2/a   pi\\           2/a\
       1 + cot |-|        2*|1 + cot |- + --||*cot(a)*cot |-|
               \2/          \        \2   4 //            \2/
−(cot⁡2(a2)−1)cot⁡(a)cot⁡2(a2)+1+(cot⁡2(a2)+1)2cot⁡(a2+π4)2(cot⁡2(a2+π4)+1)cot⁡2(a2)cot⁡(a)- \frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right) \cot{\left(a \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{2 \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \cot^{2}{\left(\frac{a}{2} \right)} \cot{\left(a \right)}} 
  /         2      \    /    pi\      2/a\    2/a   pi\ /         1     \           /a   pi\
  |1 - ------------|*sec|a - --|   sec |-|*sec |- - --|*|1 + -----------|*sec(a)*sec|- - --|
  |       2/a   pi\|    \    2 /       \2/     \2   2 / |       /    pi\|           \2   4 /
  |    sec |- - --||                                    |    sec|a - --||                   
  \        \2   2 //                                    \       \    2 //                   
- ------------------------------ + ---------------------------------------------------------
              sec(a)                                    /    pi\    /a   pi\                
                                                   4*sec|a - --|*sec|- + --|                
                                                        \    2 /    \2   4 /
−(1−2sec⁡2(a2−π2))sec⁡(a−π2)sec⁡(a)+(1+1sec⁡(a−π2))sec⁡2(a2)sec⁡(a)sec⁡2(a2−π2)sec⁡(a2−π4)4sec⁡(a2+π4)sec⁡(a−π2)- \frac{\left(1 - \frac{2}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}\right) \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}} + \frac{\left(1 + \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right) \sec^{2}{\left(\frac{a}{2} \right)} \sec{\left(a \right)} \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{4 \sec{\left(\frac{a}{2} + \frac{\pi}{4} \right)} \sec{\left(a - \frac{\pi}{2} \right)}} 
       /a\ 
  2*tan|-| 
       \2/ 
-----------
       2/a\
1 + tan |-|
        \2/
2tan⁡(a2)tan⁡2(a2)+1\frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} 
                                               /                   2 \
                                               |      /       2/a\\  |
                                             2 |      |1 + cot |-||  |
                                /       2/a\\  |      \        \4//  |
                                |1 + cot |-|| *|1 - -----------------|
                                \        \4//  |                    2|
  /           2/a\   \                         |      /        2/a\\ |
  |      8*cot |-|   |                         |    2*|-1 + cot |-|| |
  |            \4/   |                         \      \         \4// /
- |1 - --------------|*cot(a) + --------------------------------------
  |                 2|                                 2/a\           
  |    /       2/a\\ |                     8*cot(a)*cot |-|           
  |    |1 + cot |-|| |                                  \4/           
  \    \        \4// /
(1−(cot⁡2(a4)+1)22(cot⁡2(a4)−1)2)(cot⁡2(a4)+1)28cot⁡2(a4)cot⁡(a)−(1−8cot⁡2(a4)(cot⁡2(a4)+1)2)cot⁡(a)\frac{\left(1 - \frac{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}{2 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{2}}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}{8 \cot^{2}{\left(\frac{a}{4} \right)} \cot{\left(a \right)}} - \left(1 - \frac{8 \cot^{2}{\left(\frac{a}{4} \right)}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}\right) \cot{\left(a \right)} 
                           /   2            \
              /       /a\\ |sin (a)         |
     2      2*|1 - tan|-||*|------- + tan(a)|
  cos (a)     \       \2// \ cos(a)         /
- ------- - ---------------------------------
   sin(a)      /       /a\\                  
               |1 + tan|-||*(-1 + cos(2*a))  
               \       \2//
−2(1−tan⁡(a2))(sin⁡2(a)cos⁡(a)+tan⁡(a))(cos⁡(2a)−1)(tan⁡(a2)+1)−cos⁡2(a)sin⁡(a)- \frac{2 \left(1 - \tan{\left(\frac{a}{2} \right)}\right) \left(\frac{\sin^{2}{\left(a \right)}}{\cos{\left(a \right)}} + \tan{\left(a \right)}\right)}{\left(\cos{\left(2 a \right)} - 1\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)} - \frac{\cos^{2}{\left(a \right)}}{\sin{\left(a \right)}} 
     1     
-----------
   /    pi\
sec|a - --|
   \    2 /
1sec⁡(a−π2)\frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} 
                                      /                  2 \       
             2/a\                     |     /       2/a\\  |       
        8*tan |-|                   2 |     |1 + tan |-||  |       
              \4/      /       2/a\\  |     \        \4//  |       
  1 - --------------   |1 + tan |-|| *|1 - ----------------|*tan(a)
                   2   \        \4//  |                   2|       
      /       2/a\\                   |      /       2/a\\ |       
      |1 + tan |-||                   |    2*|1 - tan |-|| |       
      \        \4//                   \      \        \4// /       
- ------------------ + --------------------------------------------
        tan(a)                               2/a\                  
                                        8*tan |-|                  
                                              \4/
(1−(tan⁡2(a4)+1)22(1−tan⁡2(a4))2)(tan⁡2(a4)+1)2tan⁡(a)8tan⁡2(a4)−1−8tan⁡2(a4)(tan⁡2(a4)+1)2tan⁡(a)\frac{\left(1 - \frac{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}{2 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{2}}\right) \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \tan{\left(a \right)}}{8 \tan^{2}{\left(\frac{a}{4} \right)}} - \frac{1 - \frac{8 \tan^{2}{\left(\frac{a}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}}{\tan{\left(a \right)}} 
  /       2   \                                                                   
  |1 - -------|*csc(a)                                                            
  |       2/a\|             2/a\    2/pi   a\ /      1   \    /pi    \    /a   pi\
  |    csc |-||          csc |-|*csc |-- - -|*|1 + ------|*csc|-- - a|*csc|- + --|
  \        \2//              \2/     \2    2/ \    csc(a)/    \2     /    \2   4 /
- -------------------- + ---------------------------------------------------------
         /pi    \                                      /  a   pi\                 
      csc|-- - a|                          4*csc(a)*csc|- - + --|                 
         \2     /                                      \  2   4 /
−(1−2csc⁡2(a2))csc⁡(a)csc⁡(−a+π2)+(1+1csc⁡(a))csc⁡2(a2)csc⁡(−a+π2)csc⁡2(−a2+π2)csc⁡(a2+π4)4csc⁡(a)csc⁡(−a2+π4)- \frac{\left(1 - \frac{2}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{\left(1 + \frac{1}{\csc{\left(a \right)}}\right) \csc^{2}{\left(\frac{a}{2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)} \csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)} \csc{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{4 \csc{\left(a \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}} 
   /    pi\
cos|a - --|
   \    2 /
cos⁡(a−π2)\cos{\left(a - \frac{\pi}{2} \right)} 
           2/a\      2/a\                 /a   pi\       
  1 - 2*sin |-|   tan |-|*(1 + sin(a))*cot|- + --|*tan(a)
            \2/       \2/                 \2   4 /       
- ------------- + ---------------------------------------
      tan(a)                          4/a\               
                                 4*sin |-|               
                                       \2/
−1−2sin⁡2(a2)tan⁡(a)+(sin⁡(a)+1)tan⁡2(a2)tan⁡(a)cot⁡(a2+π4)4sin⁡4(a2)- \frac{1 - 2 \sin^{2}{\left(\frac{a}{2} \right)}}{\tan{\left(a \right)}} + \frac{\left(\sin{\left(a \right)} + 1\right) \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}} 
   csc(a)   csc(a)*sec(a)
- ------- + -------------
     2          /pi    \ 
  sec (a)    csc|-- - a| 
                \2     /
−csc⁡(a)sec⁡2(a)+csc⁡(a)sec⁡(a)csc⁡(−a+π2)- \frac{\csc{\left(a \right)}}{\sec^{2}{\left(a \right)}} + \frac{\csc{\left(a \right)} \sec{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} 
  /         2      \    /    pi\                /       2/a\\       
  |1 - ------------|*sec|a - --|                |    sec |-||       
  |       2/a   pi\|    \    2 /      2/a   pi\ |        \2/|       
  |    sec |- - --||               sec |- - --|*|1 - -------|*sec(a)
  \        \2   2 //                   \2   2 / \       2   /       
- ------------------------------ + ---------------------------------
              sec(a)                              /    pi\          
                                             2*sec|a - --|          
                                                  \    2 /
(1−sec⁡2(a2)2)sec⁡(a)sec⁡2(a2−π2)2sec⁡(a−π2)−(1−2sec⁡2(a2−π2))sec⁡(a−π2)sec⁡(a)\frac{\left(1 - \frac{\sec^{2}{\left(\frac{a}{2} \right)}}{2}\right) \sec{\left(a \right)} \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{2 \sec{\left(a - \frac{\pi}{2} \right)}} - \frac{\left(1 - \frac{2}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}\right) \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}} 
            /      1   \ /       /a\\
     2      |1 + ------|*|1 - tan|-||
  cos (a)   \    sin(a)/ \       \2//
- ------- + -------------------------
   sin(a)      /       /a\\          
               |1 + tan|-||*cos(a)   
               \       \2//
(1+1sin⁡(a))(1−tan⁡(a2))(tan⁡(a2)+1)cos⁡(a)−cos⁡2(a)sin⁡(a)\frac{\left(1 + \frac{1}{\sin{\left(a \right)}}\right) \left(1 - \tan{\left(\frac{a}{2} \right)}\right)}{\left(\tan{\left(\frac{a}{2} \right)} + 1\right) \cos{\left(a \right)}} - \frac{\cos^{2}{\left(a \right)}}{\sin{\left(a \right)}} 
               2/a\                      
            tan |-|*(1 + sin(a))*tan(a)  
  cos(a)        \2/                      
- ------ + ------------------------------
  tan(a)         8/a\    4/a\    /a   pi\
           64*cos |-|*tan |-|*tan|- + --|
                  \4/     \4/    \2   4 /
(sin⁡(a)+1)tan⁡2(a2)tan⁡(a)64cos⁡8(a4)tan⁡4(a4)tan⁡(a2+π4)−cos⁡(a)tan⁡(a)\frac{\left(\sin{\left(a \right)} + 1\right) \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(a \right)}}{64 \cos^{8}{\left(\frac{a}{4} \right)} \tan^{4}{\left(\frac{a}{4} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} - \frac{\cos{\left(a \right)}}{\tan{\left(a \right)}} 
  /         2/a\\                                 
  |1 - 2*sin |-||*sin(2*a)                        
  \          \2//             (1 + sin(a))*cos(a) 
- ------------------------ + ---------------------
              2                          2/a   pi\
         2*sin (a)           sin(2*a)*sin |- + --|
                                          \2   4 /
−(1−2sin⁡2(a2))sin⁡(2a)2sin⁡2(a)+(sin⁡(a)+1)cos⁡(a)sin⁡(2a)sin⁡2(a2+π4)- \frac{\left(1 - 2 \sin^{2}{\left(\frac{a}{2} \right)}\right) \sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)}} + \frac{\left(\sin{\left(a \right)} + 1\right) \cos{\left(a \right)}}{\sin{\left(2 a \right)} \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} 
-(1 - 2*sin(a/2)^2)*sin(2*a)/(2*sin(a)^2) + (1 + sin(a))*cos(a)/(sin(2*a)*sin(a/2 + pi/4)^2)
Respuesta numérica [src] 
cos(a)*tan(a - 3*pi/2) - cot(a - 3*pi/2)*sin(pi/2 + a)/sin(a)^2
cos(a)*tan(a - 3*pi/2) - cot(a - 3*pi/2)*sin(pi/2 + a)/sin(a)^2
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