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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
               /  pi \             
            cos|-----|*sin(pi - a) 
   2           \2 + a/             
sin (a) - -------------------------
                         /3*pi    \
          tan(pi - a)*cot|---- + a|
                         \ 2      /
−sin⁡(π−a)cos⁡(πa+2)tan⁡(π−a)cot⁡(a+3π2)+sin⁡2(a)- \frac{\sin{\left(\pi - a \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{\tan{\left(\pi - a \right)} \cot{\left(a + \frac{3 \pi}{2} \right)}} + \sin^{2}{\left(a \right)} 
sin(a)^2 - cos(pi/(2 + a))*sin(pi - a)/(tan(pi - a)*cot((3*pi)/2 + a))
Simplificación general [src] 
             /  pi \       
          cos|-----|*sin(a)
   2         \2 + a/       
sin (a) - -----------------
                  2        
               tan (a)
sin⁡2(a)−sin⁡(a)cos⁡(πa+2)tan⁡2(a)\sin^{2}{\left(a \right)} - \frac{\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{\tan^{2}{\left(a \right)}} 
sin(a)^2 - cos(pi/(2 + a))*sin(a)/tan(a)^2
Respuesta numérica [src] 
sin(a)^2 - cos(pi/(2 + a))*sin(pi - a)/(cot((3*pi)/2 + a)*tan(pi - a))
sin(a)^2 - cos(pi/(2 + a))*sin(pi - a)/(cot((3*pi)/2 + a)*tan(pi - a))
Unión de expresiones racionales [src] 
/   /2*a + 3*pi\                    /  pi \\       
|cot|----------|*sin(a)*tan(a) + cos|-----||*sin(a)
\   \    2     /                    \2 + a//       
---------------------------------------------------
                  /2*a + 3*pi\                     
               cot|----------|*tan(a)              
                  \    2     /
(sin⁡(a)tan⁡(a)cot⁡(2a+3π2)+cos⁡(πa+2))sin⁡(a)tan⁡(a)cot⁡(2a+3π2)\frac{\left(\sin{\left(a \right)} \tan{\left(a \right)} \cot{\left(\frac{2 a + 3 \pi}{2} \right)} + \cos{\left(\frac{\pi}{a + 2} \right)}\right) \sin{\left(a \right)}}{\tan{\left(a \right)} \cot{\left(\frac{2 a + 3 \pi}{2} \right)}} 
(cot((2*a + 3*pi)/2)*sin(a)*tan(a) + cos(pi/(2 + a)))*sin(a)/(cot((2*a + 3*pi)/2)*tan(a))
Combinatoria [src] 
 /     2                /  pi \\        
-|- tan (a)*sin(a) + cos|-----||*sin(a) 
 \                      \2 + a//        
----------------------------------------
                   2                    
                tan (a)
−(−sin⁡(a)tan⁡2(a)+cos⁡(πa+2))sin⁡(a)tan⁡2(a)- \frac{\left(- \sin{\left(a \right)} \tan^{2}{\left(a \right)} + \cos{\left(\frac{\pi}{a + 2} \right)}\right) \sin{\left(a \right)}}{\tan^{2}{\left(a \right)}} 
-(-tan(a)^2*sin(a) + cos(pi/(2 + a)))*sin(a)/tan(a)^2
Denominador racional [src] 
   2       2         /  pi \       
sin (a)*tan (a) - cos|-----|*sin(a)
                     \2 + a/       
-----------------------------------
                 2                 
              tan (a)
sin⁡2(a)tan⁡2(a)−sin⁡(a)cos⁡(πa+2)tan⁡2(a)\frac{\sin^{2}{\left(a \right)} \tan^{2}{\left(a \right)} - \sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{\tan^{2}{\left(a \right)}} 
(sin(a)^2*tan(a)^2 - cos(pi/(2 + a))*sin(a))/tan(a)^2
Denominador común [src] 
             /  pi \            
          cos|-----|*sin(pi - a)
   2         \2 + a/            
sin (a) + ----------------------
            tan(a)*tan(pi - a)
sin⁡2(a)+sin⁡(π−a)cos⁡(πa+2)tan⁡(a)tan⁡(π−a)\sin^{2}{\left(a \right)} + \frac{\sin{\left(\pi - a \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{\tan{\left(a \right)} \tan{\left(\pi - a \right)}} 
sin(a)^2 + cos(pi/(2 + a))*sin(pi - a)/(tan(a)*tan(pi - a))
Potencias [src] 
                      /  pi*I    -pi*I \                                                          
                      | -----    ------|                                                          
                      | 2 + a    2 + a |                                                          
                  2   |e        e      | /   I*(a - pi)    I*(pi - a)\ / I*(pi - a)    I*(a - pi)\
  /   -I*a    I*a\    |------ + -------|*\- e           + e          /*\e           + e          /
  \- e     + e   /    \  2         2   /                                                          
- ----------------- - ----------------------------------------------------------------------------
          4                                /   I*(pi - a)    I*(a - pi)\                          
                                         2*\- e           + e          /*tan(a)
−(eia−e−ia)24−(ei(π−a)−ei(a−π))(ei(π−a)+ei(a−π))(eiπa+22+e−iπa+22)2(−ei(π−a)+ei(a−π))tan⁡(a)- \frac{\left(e^{i a} - e^{- i a}\right)^{2}}{4} - \frac{\left(e^{i \left(\pi - a\right)} - e^{i \left(a - \pi\right)}\right) \left(e^{i \left(\pi - a\right)} + e^{i \left(a - \pi\right)}\right) \left(\frac{e^{\frac{i \pi}{a + 2}}}{2} + \frac{e^{- \frac{i \pi}{a + 2}}}{2}\right)}{2 \left(- e^{i \left(\pi - a\right)} + e^{i \left(a - \pi\right)}\right) \tan{\left(a \right)}} 
             /  pi \       
          cos|-----|*sin(a)
   2         \2 + a/       
sin (a) - -----------------
                  2        
               tan (a)
sin⁡2(a)−sin⁡(a)cos⁡(πa+2)tan⁡2(a)\sin^{2}{\left(a \right)} - \frac{\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{\tan^{2}{\left(a \right)}} 
sin(a)^2 - cos(pi/(2 + a))*sin(a)/tan(a)^2
Abrimos la expresión [src] 
               /  pi \             
            cos|-----|*sin(pi - a) 
   2           \2 + a/             
sin (a) - -------------------------
             /3*pi    \            
          cot|---- + a|*tan(pi - a)
             \ 2      /
sin⁡2(a)−sin⁡(π−a)cos⁡(πa+2)tan⁡(π−a)cot⁡(a+3π2)\sin^{2}{\left(a \right)} - \frac{\sin{\left(\pi - a \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{\tan{\left(\pi - a \right)} \cot{\left(a + \frac{3 \pi}{2} \right)}} 
             /  pi \       
          cos|-----|*sin(a)
   2         \2 + a/       
sin (a) - -----------------
                  2        
               tan (a)
sin⁡2(a)−sin⁡(a)cos⁡(πa+2)tan⁡2(a)\sin^{2}{\left(a \right)} - \frac{\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{\tan^{2}{\left(a \right)}} 
sin(a)^2 - cos(pi/(2 + a))*sin(a)/tan(a)^2
Parte trigonométrica [src] 
                 /   2/    pi   \      2/    pi   \\    /a\    /a\
               2*|cos |---------| - sin |---------||*cos|-|*sin|-|
1 - cos(2*a)     \    \2*(2 + a)/       \2*(2 + a)//    \2/    \2/
------------ - ---------------------------------------------------
     2                                  2                         
                                     tan (a)
1−cos⁡(2a)2−2(−sin⁡2(π2(a+2))+cos⁡2(π2(a+2)))sin⁡(a2)cos⁡(a2)tan⁡2(a)\frac{1 - \cos{\left(2 a \right)}}{2} - \frac{2 \left(- \sin^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + \cos^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right) \sin{\left(\frac{a}{2} \right)} \cos{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(a \right)}} 
                    2    /   2/    pi   \      2/  pi       pi   \\    /a\    /a   pi\
               2*cos (a)*|cos |---------| - cos |- -- + ---------||*cos|-|*cos|- - --|
1   cos(2*a)             \    \2*(2 + a)/       \  2    2*(2 + a)//    \2/    \2   2 /
- - -------- - -----------------------------------------------------------------------
2      2                                        2/    pi\                             
                                             cos |a - --|                             
                                                 \    2 /
−2(cos⁡2(π2(a+2))−cos⁡2(−π2+π2(a+2)))cos⁡(a2)cos⁡2(a)cos⁡(a2−π2)cos⁡2(a−π2)−cos⁡(2a)2+12- \frac{2 \left(\cos^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - \cos^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{2 \left(a + 2\right)} \right)}\right) \cos{\left(\frac{a}{2} \right)} \cos^{2}{\left(a \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a - \frac{\pi}{2} \right)}} - \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2} 
       2/a\                     /       2/    pi   \\              
  4*tan |-|                   2*|1 - tan |---------||              
        \2/                     \        \2*(2 + a)//              
-------------- - --------------------------------------------------
             2   /       1   \ /       2/    pi   \\    2       /a\
/       2/a\\    |1 + -------|*|1 + tan |---------||*tan (a)*tan|-|
|1 + tan |-||    |       2/a\| \        \2*(2 + a)//            \2/
\        \2//    |    tan |-||                                     
                 \        \2//
4tan⁡2(a2)(tan⁡2(a2)+1)2−2(1−tan⁡2(π2(a+2)))(1+1tan⁡2(a2))(tan⁡2(π2(a+2))+1)tan⁡(a2)tan⁡2(a)\frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - \frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right)}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(a \right)}} 
                                  2                          
       2/a\          /       2/a\\  /       2/    pi   \\    
  4*tan |-|          |1 - tan |-|| *|1 - tan |---------||    
        \2/          \        \2//  \        \2*(2 + a)//    
-------------- - --------------------------------------------
             2     /       2/a\\ /       2/    pi   \\    /a\
/       2/a\\    2*|1 + tan |-||*|1 + tan |---------||*tan|-|
|1 + tan |-||      \        \2// \        \2*(2 + a)//    \2/
\        \2//
−(1−tan⁡2(a2))2(1−tan⁡2(π2(a+2)))2(tan⁡2(a2)+1)(tan⁡2(π2(a+2))+1)tan⁡(a2)+4tan⁡2(a2)(tan⁡2(a2)+1)2- \frac{\left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right)}{2 \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \tan{\left(\frac{a}{2} \right)}} + \frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} 
                    4/a\ /       2/a\\    /  pi \    /a\
               4*cos |-|*|1 - tan |-||*cos|-----|*tan|-|
1   cos(2*a)         \4/ \        \4//    \2 + a/    \4/
- - -------- - -----------------------------------------
2      2                           2                    
                                tan (a)
−4(1−tan⁡2(a4))cos⁡4(a4)cos⁡(πa+2)tan⁡(a4)tan⁡2(a)−cos⁡(2a)2+12- \frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right) \cos^{4}{\left(\frac{a}{4} \right)} \cos{\left(\frac{\pi}{a + 2} \right)} \tan{\left(\frac{a}{4} \right)}}{\tan^{2}{\left(a \right)}} - \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2} 
   1                 csc(a)           
------- - ----------------------------
   2         2/pi    \    /pi     pi \
csc (a)   csc |-- - a|*csc|-- - -----|
              \2     /    \2    2 + a/
−csc⁡(a)csc⁡(π2−πa+2)csc⁡2(−a+π2)+1csc⁡2(a)- \frac{\csc{\left(a \right)}}{\csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 2} \right)} \csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{2}{\left(a \right)}} 
       2/a\          /       2/    pi   \\           /a\   
  4*tan |-|        2*|1 - tan |---------||*cot(a)*cot|-|   
        \2/          \        \2*(2 + a)//           \2/   
-------------- - ------------------------------------------
             2   /       2/a\\ /       2/    pi   \\       
/       2/a\\    |1 + cot |-||*|1 + tan |---------||*tan(a)
|1 + tan |-||    \        \2// \        \2*(2 + a)//       
\        \2//
−2(1−tan⁡2(π2(a+2)))cot⁡(a2)cot⁡(a)(tan⁡2(π2(a+2))+1)(cot⁡2(a2)+1)tan⁡(a)+4tan⁡2(a2)(tan⁡2(a2)+1)2- \frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right) \cot{\left(\frac{a}{2} \right)} \cot{\left(a \right)}}{\left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(a \right)}} + \frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} 
                           2    /         1                    1       \
                      2*csc (a)*|-------------------- - ---------------|
                                |   2/pi       pi   \      2/    pi   \|
                                |csc |-- - ---------|   csc |---------||
1          1                    \    \2    2*(2 + a)/       \2*(2 + a)//
- - --------------- - --------------------------------------------------
2        /pi      \               /a\    2/pi    \    /pi   a\          
    2*csc|-- - 2*a|            csc|-|*csc |-- - a|*csc|-- - -|          
         \2       /               \2/     \2     /    \2    2/
−2(1csc⁡2(π2−π2(a+2))−1csc⁡2(π2(a+2)))csc⁡2(a)csc⁡(a2)csc⁡2(−a+π2)csc⁡(−a2+π2)+12−12csc⁡(−2a+π2)- \frac{2 \left(\frac{1}{\csc^{2}{\left(\frac{\pi}{2} - \frac{\pi}{2 \left(a + 2\right)} \right)}} - \frac{1}{\csc^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}}\right) \csc^{2}{\left(a \right)}}{\csc{\left(\frac{a}{2} \right)} \csc^{2}{\left(- a + \frac{\pi}{2} \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + \frac{1}{2} - \frac{1}{2 \csc{\left(- 2 a + \frac{\pi}{2} \right)}} 
                                  2                          
       2/a\         /        2/a\\  /        2/    pi   \\   
  4*cot |-|         |-1 + cot |-|| *|-1 + cot |---------||   
        \2/         \         \2//  \         \2*(2 + a)//   
-------------- - --------------------------------------------
             2     /       2/a\\ /       2/    pi   \\    /a\
/       2/a\\    2*|1 + cot |-||*|1 + cot |---------||*cot|-|
|1 + cot |-||      \        \2// \        \2*(2 + a)//    \2/
\        \2//
−(cot⁡2(a2)−1)2(cot⁡2(π2(a+2))−1)2(cot⁡2(a2)+1)(cot⁡2(π2(a+2))+1)cot⁡(a2)+4cot⁡2(a2)(cot⁡2(a2)+1)2- \frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right)}{2 \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \cot{\left(\frac{a}{2} \right)}} + \frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} 
                                      /                     2                         \       
                                      |/       2/    pi   \\           2/    pi   \   |       
                                      ||1 - tan |---------||      4*tan |---------|   |       
                        /       2/a\\ |\        \4*(2 + a)//            \4*(2 + a)/   |    /a\
                      4*|1 - tan |-||*|---------------------- - ----------------------|*tan|-|
                        \        \4// |                     2                        2|    \4/
                                      |/       2/    pi   \\    /       2/    pi   \\ |       
             2                        ||1 + tan |---------||    |1 + tan |---------|| |       
1     1 - tan (a)                     \\        \4*(2 + a)//    \        \4*(2 + a)// /       
- - --------------- - ------------------------------------------------------------------------
2     /       2   \                                         2                                 
    2*\1 + tan (a)/                            /       2/a\\     2                            
                                               |1 + tan |-|| *tan (a)                         
                                               \        \4//
−4(1−tan⁡2(a4))((1−tan⁡2(π4(a+2)))2(tan⁡2(π4(a+2))+1)2−4tan⁡2(π4(a+2))(tan⁡2(π4(a+2))+1)2)tan⁡(a4)(tan⁡2(a4)+1)2tan⁡2(a)−1−tan⁡2(a)2(tan⁡2(a)+1)+12- \frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right) \left(\frac{\left(1 - \tan^{2}{\left(\frac{\pi}{4 \left(a + 2\right)} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{\pi}{4 \left(a + 2\right)} \right)} + 1\right)^{2}} - \frac{4 \tan^{2}{\left(\frac{\pi}{4 \left(a + 2\right)} \right)}}{\left(\tan^{2}{\left(\frac{\pi}{4 \left(a + 2\right)} \right)} + 1\right)^{2}}\right) \tan{\left(\frac{a}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \tan^{2}{\left(a \right)}} - \frac{1 - \tan^{2}{\left(a \right)}}{2 \left(\tan^{2}{\left(a \right)} + 1\right)} + \frac{1}{2} 
             2/    pi\    /pi     pi \
          sin |a + --|*sin|-- + -----|
   2          \    2 /    \2    2 + a/
sin (a) - ----------------------------
                     sin(a)
sin⁡2(a)−sin⁡(π2+πa+2)sin⁡2(a+π2)sin⁡(a)\sin^{2}{\left(a \right)} - \frac{\sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)} \sin^{2}{\left(a + \frac{\pi}{2} \right)}}{\sin{\left(a \right)}} 
             2       /  pi \
          cos (a)*cos|-----|
   2                 \2 + a/
sin (a) - ------------------
                sin(a)
sin⁡2(a)−cos⁡2(a)cos⁡(πa+2)sin⁡(a)\sin^{2}{\left(a \right)} - \frac{\cos^{2}{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{\sin{\left(a \right)}} 
                     /pi    \    
                  sec|-- - a|    
     1               \2     /    
------------ - ------------------
   2/    pi\      2       /  pi \
sec |a - --|   sec (a)*sec|-----|
    \    2 /              \2 + a/
1sec⁡2(a−π2)−sec⁡(−a+π2)sec⁡2(a)sec⁡(πa+2)\frac{1}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} - \frac{\sec{\left(- a + \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)} \sec{\left(\frac{\pi}{a + 2} \right)}} 
                               2           
               /          2/a\\     /  pi \
               |-1 + 2*sin |-|| *cos|-----|
1   cos(2*a)   \           \2//     \2 + a/
- - -------- - ----------------------------
2      2                  /a\    /a\       
                     2*cos|-|*sin|-|       
                          \2/    \2/
−(2sin⁡2(a2)−1)2cos⁡(πa+2)2sin⁡(a2)cos⁡(a2)−cos⁡(2a)2+12- \frac{\left(2 \sin^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2} \cos{\left(\frac{\pi}{a + 2} \right)}}{2 \sin{\left(\frac{a}{2} \right)} \cos{\left(\frac{a}{2} \right)}} - \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2} 
             2       /  pi \
          cos (a)*cos|-----|
   2                 \2 + a/
sin (a) - ------------------
                /    pi\    
             cos|a - --|    
                \    2 /
sin⁡2(a)−cos⁡2(a)cos⁡(πa+2)cos⁡(a−π2)\sin^{2}{\left(a \right)} - \frac{\cos^{2}{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} 
                     /    pi\    
                  sec|a - --|    
     1               \    2 /    
------------ - ------------------
   2/    pi\      2       /  pi \
sec |a - --|   sec (a)*sec|-----|
    \    2 /              \2 + a/
1sec⁡2(a−π2)−sec⁡(a−π2)sec⁡2(a)sec⁡(πa+2)\frac{1}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} - \frac{\sec{\left(a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)} \sec{\left(\frac{\pi}{a + 2} \right)}} 
       2/a\                2    /        2/    pi   \\     
  4*cot |-|           2*cot (a)*|-1 + cot |---------||     
        \2/                     \         \2*(2 + a)//     
-------------- - ------------------------------------------
             2   /       1   \ /       2/    pi   \\    /a\
/       2/a\\    |1 + -------|*|1 + cot |---------||*cot|-|
|1 + cot |-||    |       2/a\| \        \2*(2 + a)//    \2/
\        \2//    |    cot |-||                             
                 \        \2//
4cot⁡2(a2)(cot⁡2(a2)+1)2−2(cot⁡2(π2(a+2))−1)cot⁡2(a)(1+1cot⁡2(a2))(cot⁡2(π2(a+2))+1)cot⁡(a2)\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \cot^{2}{\left(a \right)}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \cot{\left(\frac{a}{2} \right)}} 
                      2/    pi\ /       1                    1           \
                 2*sec |a - --|*|--------------- - ----------------------|
                       \    2 / |   2/    pi   \      2/  pi       pi   \|
                                |sec |---------|   sec |- -- + ---------||
1       1                       \    \2*(2 + a)/       \  2    2*(2 + a)//
- - ---------- - ---------------------------------------------------------
2   2*sec(2*a)                      2       /a\    /a   pi\               
                                 sec (a)*sec|-|*sec|- - --|               
                                            \2/    \2   2 /
−2(−1sec⁡2(−π2+π2(a+2))+1sec⁡2(π2(a+2)))sec⁡2(a−π2)sec⁡(a2)sec⁡2(a)sec⁡(a2−π2)+12−12sec⁡(2a)- \frac{2 \left(- \frac{1}{\sec^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{2 \left(a + 2\right)} \right)}} + \frac{1}{\sec^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}}\right) \sec^{2}{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(\frac{a}{2} \right)} \sec^{2}{\left(a \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + \frac{1}{2} - \frac{1}{2 \sec{\left(2 a \right)}} 
                  2       /  pi \
               cos (a)*cos|-----|
   2/    pi\              \2 + a/
cos |a - --| - ------------------
    \    2 /         /    pi\    
                  cos|a - --|    
                     \    2 /
−cos⁡2(a)cos⁡(πa+2)cos⁡(a−π2)+cos⁡2(a−π2)- \frac{\cos^{2}{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} + \cos^{2}{\left(a - \frac{\pi}{2} \right)} 
                           2/    pi\         
                        sec |a - --|         
     1                      \    2 /         
------------ - ------------------------------
   2/    pi\      2       /  pi \    /pi    \
sec |a - --|   sec (a)*sec|-----|*sec|-- - a|
    \    2 /              \2 + a/    \2     /
1sec⁡2(a−π2)−sec⁡2(a−π2)sec⁡2(a)sec⁡(πa+2)sec⁡(−a+π2)\frac{1}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} - \frac{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)} \sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(- a + \frac{\pi}{2} \right)}} 
       /pi      \      2      /   2/pi       pi   \      2/    pi   \\    /a\    /pi   a\
    sin|-- + 2*a|   sin (2*a)*|sin |-- + ---------| - sin |---------||*sin|-|*sin|-- + -|
1      \2       /             \    \2    2*(2 + a)/       \2*(2 + a)//    \2/    \2    2/
- - ------------- - ---------------------------------------------------------------------
2         2                                            4                                 
                                                  2*sin (a)
−(−sin⁡2(π2(a+2))+sin⁡2(π2+π2(a+2)))sin⁡(a2)sin⁡2(2a)sin⁡(a2+π2)2sin⁡4(a)−sin⁡(2a+π2)2+12- \frac{\left(- \sin^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + \sin^{2}{\left(\frac{\pi}{2} + \frac{\pi}{2 \left(a + 2\right)} \right)}\right) \sin{\left(\frac{a}{2} \right)} \sin^{2}{\left(2 a \right)} \sin{\left(\frac{a}{2} + \frac{\pi}{2} \right)}}{2 \sin^{4}{\left(a \right)}} - \frac{\sin{\left(2 a + \frac{\pi}{2} \right)}}{2} + \frac{1}{2} 
   2         2       /  pi \       
sin (a) - cos (a)*cos|-----|*csc(a)
                     \2 + a/
sin⁡2(a)−cos⁡2(a)cos⁡(πa+2)csc⁡(a)\sin^{2}{\left(a \right)} - \cos^{2}{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} \csc{\left(a \right)} 
   1            csc(a)      
------- - ------------------
   2         2       /  pi \
csc (a)   sec (a)*sec|-----|
                     \2 + a/
−csc⁡(a)sec⁡2(a)sec⁡(πa+2)+1csc⁡2(a)- \frac{\csc{\left(a \right)}}{\sec^{2}{\left(a \right)} \sec{\left(\frac{\pi}{a + 2} \right)}} + \frac{1}{\csc^{2}{\left(a \right)}} 
             2       /pi     pi \
          cos (a)*sin|-- + -----|
   2                 \2    2 + a/
sin (a) - -----------------------
                   sin(a)
sin⁡2(a)−sin⁡(π2+πa+2)cos⁡2(a)sin⁡(a)\sin^{2}{\left(a \right)} - \frac{\sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)} \cos^{2}{\left(a \right)}}{\sin{\left(a \right)}} 
                                               /                      2                         \       
                                               |/        2/    pi   \\           2/    pi   \   |       
                                               ||-1 + cot |---------||      4*cot |---------|   |       
                           2    /        2/a\\ |\         \4*(2 + a)//            \4*(2 + a)/   |    /a\
                      4*cot (a)*|-1 + cot |-||*|----------------------- - ----------------------|*cot|-|
                                \         \4// |                      2                        2|    \4/
                                               | /       2/    pi   \\    /       2/    pi   \\ |       
              2                                | |1 + cot |---------||    |1 + cot |---------|| |       
1     -1 + cot (a)                             \ \        \4*(2 + a)//    \        \4*(2 + a)// /       
- - --------------- - ----------------------------------------------------------------------------------
2     /       2   \                                                  2                                  
    2*\1 + cot (a)/                                     /       2/a\\                                   
                                                        |1 + cot |-||                                   
                                                        \        \4//
−4((cot⁡2(π4(a+2))−1)2(cot⁡2(π4(a+2))+1)2−4cot⁡2(π4(a+2))(cot⁡2(π4(a+2))+1)2)(cot⁡2(a4)−1)cot⁡(a4)cot⁡2(a)(cot⁡2(a4)+1)2−cot⁡2(a)−12(cot⁡2(a)+1)+12- \frac{4 \left(\frac{\left(\cot^{2}{\left(\frac{\pi}{4 \left(a + 2\right)} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{\pi}{4 \left(a + 2\right)} \right)} + 1\right)^{2}} - \frac{4 \cot^{2}{\left(\frac{\pi}{4 \left(a + 2\right)} \right)}}{\left(\cot^{2}{\left(\frac{\pi}{4 \left(a + 2\right)} \right)} + 1\right)^{2}}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right) \cot{\left(\frac{a}{4} \right)} \cot^{2}{\left(a \right)}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}} - \frac{\cot^{2}{\left(a \right)} - 1}{2 \left(\cot^{2}{\left(a \right)} + 1\right)} + \frac{1}{2} 
             2/    pi\    /  pi \
          sin |a + --|*cos|-----|
   2          \    2 /    \2 + a/
sin (a) - -----------------------
                   sin(a)
sin⁡2(a)−sin⁡2(a+π2)cos⁡(πa+2)sin⁡(a)\sin^{2}{\left(a \right)} - \frac{\sin^{2}{\left(a + \frac{\pi}{2} \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{\sin{\left(a \right)}} 
                            2                                              
               /       2/a\\     2/a\    2/    pi   \ /       2/    pi   \\
               |1 - tan |-|| *cos |-|*cos |---------|*|1 - tan |---------||
1 - cos(2*a)   \        \2//      \2/     \2*(2 + a)/ \        \2*(2 + a)//
------------ - ------------------------------------------------------------
     2                                        /a\                          
                                         2*tan|-|                          
                                              \2/
1−cos⁡(2a)2−(1−tan⁡2(a2))2(1−tan⁡2(π2(a+2)))cos⁡2(a2)cos⁡2(π2(a+2))2tan⁡(a2)\frac{1 - \cos{\left(2 a \right)}}{2} - \frac{\left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right) \cos^{2}{\left(\frac{a}{2} \right)} \cos^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}}{2 \tan{\left(\frac{a}{2} \right)}} 
                         /  pi \            
               cos(a)*cos|-----|*cos(pi + a)
   2/    pi\             \2 + a/            
cos |a - --| + -----------------------------
    \    2 /               sin(a)
cos⁡2(a−π2)+cos⁡(a)cos⁡(πa+2)cos⁡(a+π)sin⁡(a)\cos^{2}{\left(a - \frac{\pi}{2} \right)} + \frac{\cos{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(a + \pi \right)}}{\sin{\left(a \right)}} 
                             2                                                      
               /        2/a\\     2/a\    2/    pi   \ /        2/    pi   \\    /a\
               |-1 + cot |-|| *sin |-|*sin |---------|*|-1 + cot |---------||*tan|-|
1 - cos(2*a)   \         \2//      \2/     \2*(2 + a)/ \         \2*(2 + a)//    \2/
------------ - ---------------------------------------------------------------------
     2                                           2
1−cos⁡(2a)2−(cot⁡2(a2)−1)2(cot⁡2(π2(a+2))−1)sin⁡2(a2)sin⁡2(π2(a+2))tan⁡(a2)2\frac{1 - \cos{\left(2 a \right)}}{2} - \frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \sin^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} \tan{\left(\frac{a}{2} \right)}}{2} 
1   cos(2*a)        2       4/a\ /        2/a\\    /  pi \    /a\
- - -------- - 4*cot (a)*sin |-|*|-1 + cot |-||*cos|-----|*cot|-|
2      2                     \4/ \         \4//    \2 + a/    \4/
−4(cot⁡2(a4)−1)sin⁡4(a4)cos⁡(πa+2)cot⁡(a4)cot⁡2(a)−cos⁡(2a)2+12- 4 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right) \sin^{4}{\left(\frac{a}{4} \right)} \cos{\left(\frac{\pi}{a + 2} \right)} \cot{\left(\frac{a}{4} \right)} \cot^{2}{\left(a \right)} - \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2} 
       2/a\          /        2/    pi   \\           /a\  
  4*cot |-|        2*|-1 + cot |---------||*cot(a)*tan|-|  
        \2/          \         \2*(2 + a)//           \2/  
-------------- - ------------------------------------------
             2   /       2/    pi   \\ /       2/a\\       
/       2/a\\    |1 + cot |---------||*|1 + tan |-||*tan(a)
|1 + cot |-||    \        \2*(2 + a)// \        \2//       
\        \2//
4cot⁡2(a2)(cot⁡2(a2)+1)2−2(cot⁡2(π2(a+2))−1)tan⁡(a2)cot⁡(a)(tan⁡2(a2)+1)(cot⁡2(π2(a+2))+1)tan⁡(a)\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \tan{\left(\frac{a}{2} \right)} \cot{\left(a \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \tan{\left(a \right)}} 
             /  pi \       
          cos|-----|*sin(a)
   2         \2 + a/       
sin (a) - -----------------
                  2        
               tan (a)
sin⁡2(a)−sin⁡(a)cos⁡(πa+2)tan⁡2(a)\sin^{2}{\left(a \right)} - \frac{\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{\tan^{2}{\left(a \right)}} 
sin(a)^2 - cos(pi/(2 + a))*sin(a)/tan(a)^2
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               /  pi \             
            cos|-----|*sin(pi - a) 
   2           \2 + a/             
sin (a) - -------------------------
             /3*pi    \            
          cot|---- + a|*tan(pi - a)
             \ 2      /
sin⁡2(a)−sin⁡(π−a)cos⁡(πa+2)tan⁡(π−a)cot⁡(a+3π2)\sin^{2}{\left(a \right)} - \frac{\sin{\left(\pi - a \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{\tan{\left(\pi - a \right)} \cot{\left(a + \frac{3 \pi}{2} \right)}} 
sin(a)^2 - cos(pi/(2 + a))*sin(pi - a)/(cot((3*pi)/2 + a)*tan(pi - a))
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