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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   /pi    \          
cos|-- + a|*(-cot(a))
   \2     /          
---------------------
         /  pi \     
      sin|-----|     
         \2 - a/
cos⁡(a+π2)(−cot⁡(a))sin⁡(π2−a)\frac{\cos{\left(a + \frac{\pi}{2} \right)} \left(- \cot{\left(a \right)}\right)}{\sin{\left(\frac{\pi}{2 - a} \right)}} 
(cos(pi/2 + a)*(-cot(a)))/sin(pi/(2 - a))
Simplificación general [src] 
  -cos(a)  
-----------
   /  pi  \
sin|------|
   \-2 + a/
−cos⁡(a)sin⁡(πa−2)- \frac{\cos{\left(a \right)}}{\sin{\left(\frac{\pi}{a - 2} \right)}} 
-cos(a)/sin(pi/(-2 + a))
Unión de expresiones racionales [src] 
    /pi + 2*a\        
-cos|--------|*cot(a) 
    \   2    /        
----------------------
         /  pi \      
      sin|-----|      
         \2 - a/
−cos⁡(2a+π2)cot⁡(a)sin⁡(π2−a)- \frac{\cos{\left(\frac{2 a + \pi}{2} \right)} \cot{\left(a \right)}}{\sin{\left(\frac{\pi}{2 - a} \right)}} 
-cos((pi + 2*a)/2)*cot(a)/sin(pi/(2 - a))
Respuesta numérica [src] 
-cos(pi/2 + a)*cot(a)/sin(pi/(2 - a))
-cos(pi/2 + a)*cot(a)/sin(pi/(2 - a))
Combinatoria [src] 
cot(a)*sin(a)
-------------
     /  pi \ 
  sin|-----| 
     \2 - a/
sin⁡(a)cot⁡(a)sin⁡(π2−a)\frac{\sin{\left(a \right)} \cot{\left(a \right)}}{\sin{\left(\frac{\pi}{2 - a} \right)}} 
cot(a)*sin(a)/sin(pi/(2 - a))
Denominador común [src] 
cot(a)*sin(a)
-------------
     /  pi \ 
  sin|-----| 
     \2 - a/
sin⁡(a)cot⁡(a)sin⁡(π2−a)\frac{\sin{\left(a \right)} \cot{\left(a \right)}}{\sin{\left(\frac{\pi}{2 - a} \right)}} 
cot(a)*sin(a)/sin(pi/(2 - a))
Potencias [src] 
cot(a)*sin(a)
-------------
     /  pi \ 
  sin|-----| 
     \2 - a/
sin⁡(a)cot⁡(a)sin⁡(π2−a)\frac{\sin{\left(a \right)} \cot{\left(a \right)}}{\sin{\left(\frac{\pi}{2 - a} \right)}} 
     /   /    pi\      /     pi\\       
     | I*|a + --|    I*|-a - --||       
     |   \    2 /      \     2 /|       
     |e             e           |       
-2*I*|----------- + ------------|*cot(a)
     \     2             2      /       
----------------------------------------
              -pi*I      pi*I           
              ------    -----           
              2 - a     2 - a           
           - e       + e
−2i(ei(−a−π2)2+ei(a+π2)2)cot⁡(a)eiπ2−a−e−iπ2−a- \frac{2 i \left(\frac{e^{i \left(- a - \frac{\pi}{2}\right)}}{2} + \frac{e^{i \left(a + \frac{\pi}{2}\right)}}{2}\right) \cot{\left(a \right)}}{e^{\frac{i \pi}{2 - a}} - e^{- \frac{i \pi}{2 - a}}} 
-2*i*(exp(i*(a + pi/2))/2 + exp(i*(-a - pi/2))/2)*cot(a)/(-exp(-pi*i/(2 - a)) + exp(pi*i/(2 - a)))
Denominador racional [src] 
   /    pi\       
cos|a + --|*cot(a)
   \    2 /       
------------------
      /  pi  \    
   sin|------|    
      \-2 + a/
cos⁡(a+π2)cot⁡(a)sin⁡(πa−2)\frac{\cos{\left(a + \frac{\pi}{2} \right)} \cot{\left(a \right)}}{\sin{\left(\frac{\pi}{a - 2} \right)}} 
cos(a + pi/2)*cot(a)/sin(pi/(-2 + a))
Abrimos la expresión [src] 
cot(a)*sin(a)
-------------
     /  pi \ 
  sin|-----| 
     \2 - a/
sin⁡(a)cot⁡(a)sin⁡(π2−a)\frac{\sin{\left(a \right)} \cot{\left(a \right)}}{\sin{\left(\frac{\pi}{2 - a} \right)}} 
cot(a)*sin(a)/sin(pi/(2 - a))
Compilar la expresión [src] 
    /pi    \        
-cos|-- + a|*cot(a) 
    \2     /        
--------------------
        /  pi \     
     sin|-----|     
        \2 - a/
−cos⁡(a+π2)cot⁡(a)sin⁡(π2−a)- \frac{\cos{\left(a + \frac{\pi}{2} \right)} \cot{\left(a \right)}}{\sin{\left(\frac{\pi}{2 - a} \right)}} 
-cos(pi/2 + a)*cot(a)/sin(pi/(2 - a))
Parte trigonométrica [src] 
              /a\    /a   pi\ 
 -2*cos(a)*cos|-|*cos|- - --| 
              \2/    \2   2 / 
------------------------------
   /    pi\    /  pi     pi  \
cos|a - --|*cos|- -- + ------|
   \    2 /    \  2    -2 + a/
−2cos⁡(a2)cos⁡(a)cos⁡(a2−π2)cos⁡(−π2+πa−2)cos⁡(a−π2)- \frac{2 \cos{\left(\frac{a}{2} \right)} \cos{\left(a \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)}} 
   /    pi\    /  pi     pi \
sec|a - --|*sec|- -- + -----|
   \    2 /    \  2    2 - a/
-----------------------------
        csc(a)*sec(a)
sec⁡(−π2+π2−a)sec⁡(a−π2)csc⁡(a)sec⁡(a)\frac{\sec{\left(- \frac{\pi}{2} + \frac{\pi}{2 - a} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}{\csc{\left(a \right)} \sec{\left(a \right)}} 
 /       2/    pi   \\ /       2/a   pi\\ 
-|1 + tan |---------||*|1 - tan |- + --|| 
 \        \2*(2 - a)// \        \2   4 // 
------------------------------------------
  /       2/a   pi\\           /    pi   \
2*|1 + tan |- + --||*tan(a)*tan|---------|
  \        \2   4 //           \2*(2 - a)/
−(1−tan⁡2(a2+π4))(tan⁡2(π2(2−a))+1)2(tan⁡2(a2+π4)+1)tan⁡(a)tan⁡(π2(2−a))- \frac{\left(1 - \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(2 - a\right)} \right)} + 1\right)}{2 \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \tan{\left(a \right)} \tan{\left(\frac{\pi}{2 \left(2 - a\right)} \right)}} 
-sin(2*a)*sin(pi + a) 
----------------------
      2       /  pi \ 
 2*sin (a)*sin|-----| 
              \2 - a/
−sin⁡(2a)sin⁡(a+π)2sin⁡2(a)sin⁡(π2−a)- \frac{\sin{\left(2 a \right)} \sin{\left(a + \pi \right)}}{2 \sin^{2}{\left(a \right)} \sin{\left(\frac{\pi}{2 - a} \right)}} 
 /       2/    pi    \\ /       2/a\\ 
-|1 + tan |----------||*|1 - tan |-|| 
 \        \2*(-2 + a)// \        \2// 
--------------------------------------
     /       2/a\\    /    pi    \    
   2*|1 + tan |-||*tan|----------|    
     \        \2//    \2*(-2 + a)/
−(1−tan⁡2(a2))(tan⁡2(π2(a−2))+1)2(tan⁡2(a2)+1)tan⁡(π2(a−2))- \frac{\left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(a - 2\right)} \right)} + 1\right)}{2 \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(\frac{\pi}{2 \left(a - 2\right)} \right)}} 
          4/a\ /       2/a\\    /a\    
    -2*cos |-|*|1 - tan |-||*tan|-|    
           \4/ \        \4//    \4/    
---------------------------------------
   2/    pi    \           /    pi    \
cos |----------|*tan(a)*tan|----------|
    \2*(-2 + a)/           \2*(-2 + a)/
−2(1−tan⁡2(a4))cos⁡4(a4)tan⁡(a4)cos⁡2(π2(a−2))tan⁡(a)tan⁡(π2(a−2))- \frac{2 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right) \cos^{4}{\left(\frac{a}{4} \right)} \tan{\left(\frac{a}{4} \right)}}{\cos^{2}{\left(\frac{\pi}{2 \left(a - 2\right)} \right)} \tan{\left(a \right)} \tan{\left(\frac{\pi}{2 \left(a - 2\right)} \right)}} 
   /       2/    pi    \\ /       2/a\\    /a\
-2*|1 + tan |----------||*|1 - tan |-||*tan|-|
   \        \2*(-2 + a)// \        \4//    \4/
----------------------------------------------
                 2                            
    /       2/a\\            /    pi    \     
    |1 + tan |-|| *tan(a)*tan|----------|     
    \        \4//            \2*(-2 + a)/
−2(1−tan⁡2(a4))(tan⁡2(π2(a−2))+1)tan⁡(a4)(tan⁡2(a4)+1)2tan⁡(a)tan⁡(π2(a−2))- \frac{2 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(a - 2\right)} \right)} + 1\right) \tan{\left(\frac{a}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \tan{\left(a \right)} \tan{\left(\frac{\pi}{2 \left(a - 2\right)} \right)}} 
          /  pi \
cos(a)*csc|-----|
          \2 - a/
cos⁡(a)csc⁡(π2−a)\cos{\left(a \right)} \csc{\left(\frac{\pi}{2 - a} \right)} 
    /  pi  \ 
-csc|------| 
    \-2 + a/ 
-------------
    /pi    \ 
 csc|-- - a| 
    \2     /
−csc⁡(πa−2)csc⁡(−a+π2)- \frac{\csc{\left(\frac{\pi}{a - 2} \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} 
                 /  pi  \     
    -2*csc(a)*csc|------|     
                 \-2 + a/     
------------------------------
   /a\    /pi    \    /pi   a\
csc|-|*csc|-- - a|*csc|-- - -|
   \2/    \2     /    \2    2/
−2csc⁡(a)csc⁡(πa−2)csc⁡(a2)csc⁡(−a+π2)csc⁡(−a2+π2)- \frac{2 \csc{\left(a \right)} \csc{\left(\frac{\pi}{a - 2} \right)}}{\csc{\left(\frac{a}{2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} 
           /  pi  \
-cos(a)*csc|------|
           \-2 + a/
−cos⁡(a)csc⁡(πa−2)- \cos{\left(a \right)} \csc{\left(\frac{\pi}{a - 2} \right)} 
       /a\    /a\ 
 -2*cos|-|*sin|-| 
       \2/    \2/ 
------------------
   /  pi  \       
sin|------|*tan(a)
   \-2 + a/
−2sin⁡(a2)cos⁡(a2)sin⁡(πa−2)tan⁡(a)- \frac{2 \sin{\left(\frac{a}{2} \right)} \cos{\left(\frac{a}{2} \right)}}{\sin{\left(\frac{\pi}{a - 2} \right)} \tan{\left(a \right)}} 
      cos(a)     
-----------------
   /  pi     pi \
cos|- -- + -----|
   \  2    2 - a/
cos⁡(a)cos⁡(−π2+π2−a)\frac{\cos{\left(a \right)}}{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{2 - a} \right)}} 
 /       2/    pi   \\ /        2/a   pi\\        
-|1 + cot |---------||*|-1 + cot |- + --||*cot(a) 
 \        \2*(2 - a)// \         \2   4 //        
--------------------------------------------------
         /       2/a   pi\\    /    pi   \        
       2*|1 + cot |- + --||*cot|---------|        
         \        \2   4 //    \2*(2 - a)/
−(cot⁡2(π2(2−a))+1)(cot⁡2(a2+π4)−1)cot⁡(a)2(cot⁡2(a2+π4)+1)cot⁡(π2(2−a))- \frac{\left(\cot^{2}{\left(\frac{\pi}{2 \left(2 - a\right)} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right) \cot{\left(a \right)}}{2 \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \cot{\left(\frac{\pi}{2 \left(2 - a\right)} \right)}} 
   /  pi \
csc|-----|
   \2 - a/
----------
  sec(a)
csc⁡(π2−a)sec⁡(a)\frac{\csc{\left(\frac{\pi}{2 - a} \right)}}{\sec{\left(a \right)}} 
/       2/    pi   \\ /       2/a\\
|1 + tan |---------||*|1 - tan |-||
\        \2*(2 - a)// \        \2//
-----------------------------------
     /       2/a\\    /    pi   \  
   2*|1 + tan |-||*tan|---------|  
     \        \2//    \2*(2 - a)/
(1−tan⁡2(a2))(tan⁡2(π2(2−a))+1)2(tan⁡2(a2)+1)tan⁡(π2(2−a))\frac{\left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(2 - a\right)} \right)} + 1\right)}{2 \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(\frac{\pi}{2 \left(2 - a\right)} \right)}} 
    /  pi \
 csc|-----|
    \2 - a/
-----------
   /pi    \
csc|-- - a|
   \2     /
csc⁡(π2−a)csc⁡(−a+π2)\frac{\csc{\left(\frac{\pi}{2 - a} \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} 
   /       2/    pi    \\ /        2/a\\           /a\
-2*|1 + cot |----------||*|-1 + cot |-||*cot(a)*cot|-|
   \        \2*(-2 + a)// \         \4//           \4/
------------------------------------------------------
                         2                            
            /       2/a\\     /    pi    \            
            |1 + cot |-|| *cot|----------|            
            \        \4//     \2*(-2 + a)/
−2(cot⁡2(a4)−1)(cot⁡2(π2(a−2))+1)cot⁡(a4)cot⁡(a)(cot⁡2(a4)+1)2cot⁡(π2(a−2))- \frac{2 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a - 2\right)} \right)} + 1\right) \cot{\left(\frac{a}{4} \right)} \cot{\left(a \right)}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \cot{\left(\frac{\pi}{2 \left(a - 2\right)} \right)}} 
          /    pi\
cos(a)*cos|a - --|
          \    2 /
------------------
          /  pi \ 
sin(a)*sin|-----| 
          \2 - a/
cos⁡(a)cos⁡(a−π2)sin⁡(a)sin⁡(π2−a)\frac{\cos{\left(a \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{\sin{\left(a \right)} \sin{\left(\frac{\pi}{2 - a} \right)}} 
                      /        2/a   pi\\           
                      |     cos |- + --||           
    /       /    pi\\ |         \2   4 /|           
    |1 + cos|a - --||*|-1 + ------------|*cos(a)    
    \       \    2 // |        2/a   pi\|           
                      |     cos |- - --||           
                      \         \2   4 //           
----------------------------------------------------
     /    pi    \    /    pi\    /  pi       pi    \
4*cos|----------|*cos|a - --|*cos|- -- + ----------|
     \2*(-2 + a)/    \    2 /    \  2    2*(-2 + a)/
(−1+cos⁡2(a2+π4)cos⁡2(a2−π4))(cos⁡(a−π2)+1)cos⁡(a)4cos⁡(π2(a−2))cos⁡(−π2+π2(a−2))cos⁡(a−π2)\frac{\left(-1 + \frac{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}\right) \left(\cos{\left(a - \frac{\pi}{2} \right)} + 1\right) \cos{\left(a \right)}}{4 \cos{\left(\frac{\pi}{2 \left(a - 2\right)} \right)} \cos{\left(- \frac{\pi}{2} + \frac{\pi}{2 \left(a - 2\right)} \right)} \cos{\left(a - \frac{\pi}{2} \right)}} 
             /        2/a   pi\\           /    pi    \
(1 + sin(a))*|-1 + cot |- + --||*cot(a)*tan|----------|
             \         \2   4 //           \2*(-2 + a)/
-------------------------------------------------------
                        2/    pi    \                  
                   4*sin |----------|                  
                         \2*(-2 + a)/
(sin⁡(a)+1)(cot⁡2(a2+π4)−1)tan⁡(π2(a−2))cot⁡(a)4sin⁡2(π2(a−2))\frac{\left(\sin{\left(a \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right) \tan{\left(\frac{\pi}{2 \left(a - 2\right)} \right)} \cot{\left(a \right)}}{4 \sin^{2}{\left(\frac{\pi}{2 \left(a - 2\right)} \right)}} 
                        /           /a\ \                                    
                      2 |      2*tan|-| |                                    
/       2/    pi    \\  |           \2/ | /          1      \    /    pi    \
|1 + tan |----------|| *|1 + -----------|*|-1 + ------------|*tan|----------|
\        \4*(-2 + a)//  |           2/a\| |        2/a   pi\|    \2*(-2 + a)/
                        |    1 + tan |-|| |     tan |- + --||                
                        \            \2// \         \2   4 //                
-----------------------------------------------------------------------------
                                       2/    pi    \                         
                          16*tan(a)*tan |----------|                         
                                        \4*(-2 + a)/
(−1+1tan⁡2(a2+π4))(1+2tan⁡(a2)tan⁡2(a2)+1)(tan⁡2(π4(a−2))+1)2tan⁡(π2(a−2))16tan⁡(a)tan⁡2(π4(a−2))\frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{\pi}{4 \left(a - 2\right)} \right)} + 1\right)^{2} \tan{\left(\frac{\pi}{2 \left(a - 2\right)} \right)}}{16 \tan{\left(a \right)} \tan^{2}{\left(\frac{\pi}{4 \left(a - 2\right)} \right)}} 
        cos(a)*sin(a)        
-----------------------------
   /    pi\    /  pi     pi \
cos|a - --|*cos|- -- + -----|
   \    2 /    \  2    2 - a/
sin⁡(a)cos⁡(a)cos⁡(−π2+π2−a)cos⁡(a−π2)\frac{\sin{\left(a \right)} \cos{\left(a \right)}}{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{2 - a} \right)} \cos{\left(a - \frac{\pi}{2} \right)}} 
      4/a\ /        2/a\\           /a\    /    pi    \
-2*sin |-|*|-1 + cot |-||*cot(a)*cot|-|*tan|----------|
       \4/ \         \4//           \4/    \2*(-2 + a)/
-------------------------------------------------------
                       2/    pi    \                   
                    sin |----------|                   
                        \2*(-2 + a)/
−2(cot⁡2(a4)−1)sin⁡4(a4)tan⁡(π2(a−2))cot⁡(a4)cot⁡(a)sin⁡2(π2(a−2))- \frac{2 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right) \sin^{4}{\left(\frac{a}{4} \right)} \tan{\left(\frac{\pi}{2 \left(a - 2\right)} \right)} \cot{\left(\frac{a}{4} \right)} \cot{\left(a \right)}}{\sin^{2}{\left(\frac{\pi}{2 \left(a - 2\right)} \right)}} 
    /    pi\ 
-sin|a + --| 
    \    2 / 
-------------
    /  pi  \ 
 sin|------| 
    \-2 + a/
−sin⁡(a+π2)sin⁡(πa−2)- \frac{\sin{\left(a + \frac{\pi}{2} \right)}}{\sin{\left(\frac{\pi}{a - 2} \right)}} 
  cos(a)  
----------
   /  pi \
sin|-----|
   \2 - a/
cos⁡(a)sin⁡(π2−a)\frac{\cos{\left(a \right)}}{\sin{\left(\frac{\pi}{2 - a} \right)}} 
             /         2/a   pi\ \                                            
             |      csc |- + --| |                                            
/      1   \ |          \2   4 / |           /    pi    \    /pi       pi    \
|1 + ------|*|-1 + --------------|*csc(a)*csc|----------|*csc|-- - ----------|
\    csc(a)/ |        2/  a   pi\|           \2*(-2 + a)/    \2    2*(-2 + a)/
             |     csc |- - + --||                                            
             \         \  2   4 //                                            
------------------------------------------------------------------------------
                                     /pi    \                                 
                                4*csc|-- - a|                                 
                                     \2     /
(−1+csc⁡2(a2+π4)csc⁡2(−a2+π4))(1+1csc⁡(a))csc⁡(a)csc⁡(π2(a−2))csc⁡(π2−π2(a−2))4csc⁡(−a+π2)\frac{\left(-1 + \frac{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(1 + \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(a \right)} \csc{\left(\frac{\pi}{2 \left(a - 2\right)} \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{2 \left(a - 2\right)} \right)}}{4 \csc{\left(- a + \frac{\pi}{2} \right)}} 
     -cos(a)      
------------------
   /  pi     pi  \
cos|- -- + ------|
   \  2    -2 + a/
−cos⁡(a)cos⁡(−π2+πa−2)- \frac{\cos{\left(a \right)}}{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)}} 
    /  pi     pi  \ 
-sec|- -- + ------| 
    \  2    -2 + a/ 
--------------------
       sec(a)
−sec⁡(−π2+πa−2)sec⁡(a)- \frac{\sec{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)}}{\sec{\left(a \right)}} 
/       2/    pi   \\ /        2/a\\
|1 + cot |---------||*|-1 + cot |-||
\        \2*(2 - a)// \         \2//
------------------------------------
     /       2/a\\    /    pi   \   
   2*|1 + cot |-||*cot|---------|   
     \        \2//    \2*(2 - a)/
(cot⁡2(a2)−1)(cot⁡2(π2(2−a))+1)2(cot⁡2(a2)+1)cot⁡(π2(2−a))\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(2 - a\right)} \right)} + 1\right)}{2 \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \cot{\left(\frac{\pi}{2 \left(2 - a\right)} \right)}} 
  -cos(a)  
-----------
   /  pi  \
sin|------|
   \-2 + a/
−cos⁡(a)sin⁡(πa−2)- \frac{\cos{\left(a \right)}}{\sin{\left(\frac{\pi}{a - 2} \right)}} 
    /a\             /pi   a\ 
-sin|-|*sin(2*a)*sin|-- + -| 
    \2/             \2    2/ 
-----------------------------
        2       /  pi  \     
     sin (a)*sin|------|     
                \-2 + a/
−sin⁡(a2)sin⁡(2a)sin⁡(a2+π2)sin⁡2(a)sin⁡(πa−2)- \frac{\sin{\left(\frac{a}{2} \right)} \sin{\left(2 a \right)} \sin{\left(\frac{a}{2} + \frac{\pi}{2} \right)}}{\sin^{2}{\left(a \right)} \sin{\left(\frac{\pi}{a - 2} \right)}} 
          /  pi \ 
csc(a)*csc|-----| 
          \2 - a/ 
------------------
          /pi    \
sec(a)*sec|-- - a|
          \2     /
csc⁡(a)csc⁡(π2−a)sec⁡(a)sec⁡(−a+π2)\frac{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2 - a} \right)}}{\sec{\left(a \right)} \sec{\left(- a + \frac{\pi}{2} \right)}} 
   /pi     pi \
sec|-- - -----|
   \2    2 - a/
---------------
     sec(a)
sec⁡(π2−π2−a)sec⁡(a)\frac{\sec{\left(\frac{\pi}{2} - \frac{\pi}{2 - a} \right)}}{\sec{\left(a \right)}} 
 /       2/    pi    \\ /        2/a\\ 
-|1 + cot |----------||*|-1 + cot |-|| 
 \        \2*(-2 + a)// \         \2// 
---------------------------------------
      /       2/a\\    /    pi    \    
    2*|1 + cot |-||*cot|----------|    
      \        \2//    \2*(-2 + a)/
−(cot⁡2(a2)−1)(cot⁡2(π2(a−2))+1)2(cot⁡2(a2)+1)cot⁡(π2(a−2))- \frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right) \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) \cot{\left(\frac{\pi}{2 \left(a - 2\right)} \right)}} 
                   /a\    /    pi    \
-2*(1 + sin(a))*tan|-|*tan|----------|
                   \2/    \2*(-2 + a)/
--------------------------------------
                              2       
/       /  pi  \\ /       /a\\        
|1 - cos|------||*|1 + tan|-|| *tan(a)
\       \-2 + a// \       \2//
−2(sin⁡(a)+1)tan⁡(a2)tan⁡(π2(a−2))(1−cos⁡(πa−2))(tan⁡(a2)+1)2tan⁡(a)- \frac{2 \left(\sin{\left(a \right)} + 1\right) \tan{\left(\frac{a}{2} \right)} \tan{\left(\frac{\pi}{2 \left(a - 2\right)} \right)}}{\left(1 - \cos{\left(\frac{\pi}{a - 2} \right)}\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan{\left(a \right)}} 
      /    pi\    /  pi     pi  \
-2*sec|a - --|*sec|- -- + ------|
      \    2 /    \  2    -2 + a/
---------------------------------
              /a\    /a   pi\    
    sec(a)*sec|-|*sec|- - --|    
              \2/    \2   2 /
−2sec⁡(−π2+πa−2)sec⁡(a−π2)sec⁡(a2)sec⁡(a)sec⁡(a2−π2)- \frac{2 \sec{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(\frac{a}{2} \right)} \sec{\left(a \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} 
   2/    pi    \              /        2/a   pi\\           /    pi    \
tan |----------|*(1 + sin(a))*|-1 + cot |- + --||*cot(a)*tan|----------|
    \4*(-2 + a)/              \         \2   4 //           \2*(-2 + a)/
------------------------------------------------------------------------
                                4/    pi    \                           
                          16*sin |----------|                           
                                 \4*(-2 + a)/
(sin⁡(a)+1)(cot⁡2(a2+π4)−1)tan⁡2(π4(a−2))tan⁡(π2(a−2))cot⁡(a)16sin⁡4(π4(a−2))\frac{\left(\sin{\left(a \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right) \tan^{2}{\left(\frac{\pi}{4 \left(a - 2\right)} \right)} \tan{\left(\frac{\pi}{2 \left(a - 2\right)} \right)} \cot{\left(a \right)}}{16 \sin^{4}{\left(\frac{\pi}{4 \left(a - 2\right)} \right)}} 
      sin(2*a)     
-------------------
            /  pi \
2*sin(a)*sin|-----|
            \2 - a/
sin⁡(2a)2sin⁡(a)sin⁡(π2−a)\frac{\sin{\left(2 a \right)}}{2 \sin{\left(a \right)} \sin{\left(\frac{\pi}{2 - a} \right)}} 
                  /        2/a   pi\\                                                   
                  |     sec |- - --||                                                   
/         1     \ |         \2   4 /|    /    pi    \    /    pi\    /  pi       pi    \
|1 + -----------|*|-1 + ------------|*sec|----------|*sec|a - --|*sec|- -- + ----------|
|       /    pi\| |        2/a   pi\|    \2*(-2 + a)/    \    2 /    \  2    2*(-2 + a)/
|    sec|a - --|| |     sec |- + --||                                                   
\       \    2 // \         \2   4 //                                                   
----------------------------------------------------------------------------------------
                                        4*sec(a)
(1+1sec⁡(a−π2))(sec⁡2(a2−π4)sec⁡2(a2+π4)−1)sec⁡(π2(a−2))sec⁡(−π2+π2(a−2))sec⁡(a−π2)4sec⁡(a)\frac{\left(1 + \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right) \left(\frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} - 1\right) \sec{\left(\frac{\pi}{2 \left(a - 2\right)} \right)} \sec{\left(- \frac{\pi}{2} + \frac{\pi}{2 \left(a - 2\right)} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}{4 \sec{\left(a \right)}} 
                        /           /a\ \                           
                      2 |      2*cot|-| |                           
/       2/    pi    \\  |           \2/ | /        2/a   pi\\       
|1 + cot |----------|| *|1 + -----------|*|-1 + cot |- + --||*cot(a)
\        \4*(-2 + a)//  |           2/a\| \         \2   4 //       
                        |    1 + cot |-||                           
                        \            \2//                           
--------------------------------------------------------------------
                      /    pi    \    2/    pi    \                 
                16*cot|----------|*cot |----------|                 
                      \2*(-2 + a)/     \4*(-2 + a)/
(1+2cot⁡(a2)cot⁡2(a2)+1)(cot⁡2(π4(a−2))+1)2(cot⁡2(a2+π4)−1)cot⁡(a)16cot⁡2(π4(a−2))cot⁡(π2(a−2))\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{\pi}{4 \left(a - 2\right)} \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right) \cot{\left(a \right)}}{16 \cot^{2}{\left(\frac{\pi}{4 \left(a - 2\right)} \right)} \cot{\left(\frac{\pi}{2 \left(a - 2\right)} \right)}} 
             /           2       \         
             |        cos (a)    |         
(1 + sin(a))*|-1 + --------------|*sin(2*a)
             |          4/a   pi\|         
             |     4*sin |- + --||         
             \           \2   4 //         
-------------------------------------------
                2       /  pi  \           
           4*sin (a)*sin|------|           
                        \-2 + a/
(−1+cos⁡2(a)4sin⁡4(a2+π4))(sin⁡(a)+1)sin⁡(2a)4sin⁡2(a)sin⁡(πa−2)\frac{\left(-1 + \frac{\cos^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(\sin{\left(a \right)} + 1\right) \sin{\left(2 a \right)}}{4 \sin^{2}{\left(a \right)} \sin{\left(\frac{\pi}{a - 2} \right)}} 
   /    pi\
sin|a + --|
   \    2 /
-----------
    /  pi \
 sin|-----|
    \2 - a/
sin⁡(a+π2)sin⁡(π2−a)\frac{\sin{\left(a + \frac{\pi}{2} \right)}}{\sin{\left(\frac{\pi}{2 - a} \right)}} 
sin(a + pi/2)/sin(pi/(2 - a))
    © Sr Examen – Калькулятор