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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   2/3*pi    \      2/3*pi    \
sin |---- - a| + cos |---- - a|
    \ 2      /       \ 2      /
-------------------------------
       pi - a    2             
      -------*tan (pi - a)     
         2                     
      tan (a)
sin⁡2(−a+3π2)+cos⁡2(−a+3π2)π−atan⁡2(a)tan⁡2(π−a)\frac{\sin^{2}{\left(- a + \frac{3 \pi}{2} \right)} + \cos^{2}{\left(- a + \frac{3 \pi}{2} \right)}}{\frac{\pi - a}{\tan^{2}{\left(a \right)}} \tan^{2}{\left(\pi - a \right)}} 
(sin((3*pi)/2 - a)^2 + cos((3*pi)/2 - a)^2)/((((pi - a)/tan(a)^2)*tan(pi - a)^2))
Simplificación general [src] 
 -1   
------
a - pi
−1a−π- \frac{1}{a - \pi} 
-1/(a - pi)
Respuesta numérica [src] 
tan(a)^2*(cos((3*pi)/2 - a)^2 + sin((3*pi)/2 - a)^2)/((3.14159265358979 - a)*tan(pi - a)^2)
tan(a)^2*(cos((3*pi)/2 - a)^2 + sin((3*pi)/2 - a)^2)/((3.14159265358979 - a)*tan(pi - a)^2)
Combinatoria [src] 
 /   2         2   \ 
-\cos (a) + sin (a)/ 
---------------------
        a - pi
−sin⁡2(a)+cos⁡2(a)a−π- \frac{\sin^{2}{\left(a \right)} + \cos^{2}{\left(a \right)}}{a - \pi} 
-(cos(a)^2 + sin(a)^2)/(a - pi)
Unión de expresiones racionales [src] 
   2/-2*a + 3*pi\      2/-2*a + 3*pi\
cos |-----------| + sin |-----------|
    \     2     /       \     2     /
-------------------------------------
                pi - a
sin⁡2(−2a+3π2)+cos⁡2(−2a+3π2)π−a\frac{\sin^{2}{\left(\frac{- 2 a + 3 \pi}{2} \right)} + \cos^{2}{\left(\frac{- 2 a + 3 \pi}{2} \right)}}{\pi - a} 
(cos((-2*a + 3*pi)/2)^2 + sin((-2*a + 3*pi)/2)^2)/(pi - a)
Denominador común [src] 
 /   2       2         2       2   \ 
-\cos (a)*tan (a) + sin (a)*tan (a)/ 
-------------------------------------
        2                 2          
   a*tan (pi - a) - pi*tan (pi - a)
−sin⁡2(a)tan⁡2(a)+cos⁡2(a)tan⁡2(a)atan⁡2(π−a)−πtan⁡2(π−a)- \frac{\sin^{2}{\left(a \right)} \tan^{2}{\left(a \right)} + \cos^{2}{\left(a \right)} \tan^{2}{\left(a \right)}}{a \tan^{2}{\left(\pi - a \right)} - \pi \tan^{2}{\left(\pi - a \right)}} 
-(cos(a)^2*tan(a)^2 + sin(a)^2*tan(a)^2)/(a*tan(pi - a)^2 - pi*tan(pi - a)^2)
Compilar la expresión [src] 
   2    /   2/3*pi    \      2/3*pi    \\
tan (a)*|cos |---- - a| + sin |---- - a||
        \    \ 2      /       \ 2      //
-----------------------------------------
                      2                  
          (pi - a)*tan (pi - a)
(sin⁡2(−a+3π2)+cos⁡2(−a+3π2))tan⁡2(a)(π−a)tan⁡2(π−a)\frac{\left(\sin^{2}{\left(- a + \frac{3 \pi}{2} \right)} + \cos^{2}{\left(- a + \frac{3 \pi}{2} \right)}\right) \tan^{2}{\left(a \right)}}{\left(\pi - a\right) \tan^{2}{\left(\pi - a \right)}} 
tan(a)^2*(cos((3*pi)/2 - a)^2 + sin((3*pi)/2 - a)^2)/((pi - a)*tan(pi - a)^2)
Abrimos la expresión [src] 
   2         2   
cos (a)   sin (a)
------- + -------
 pi - a    pi - a
sin⁡2(a)π−a+cos⁡2(a)π−a\frac{\sin^{2}{\left(a \right)}}{\pi - a} + \frac{\cos^{2}{\left(a \right)}}{\pi - a} 
   2    /   2/3*pi    \      2/3*pi    \\
tan (a)*|sin |---- - a| + cos |---- - a||
        \    \ 2      /       \ 2      //
-----------------------------------------
                      2                  
          (pi - a)*tan (pi - a)
(sin⁡2(−a+3π2)+cos⁡2(−a+3π2))tan⁡2(a)(π−a)tan⁡2(π−a)\frac{\left(\sin^{2}{\left(- a + \frac{3 \pi}{2} \right)} + \cos^{2}{\left(- a + \frac{3 \pi}{2} \right)}\right) \tan^{2}{\left(a \right)}}{\left(\pi - a\right) \tan^{2}{\left(\pi - a \right)}} 
tan(a)^2*(sin((3*pi)/2 - a)^2 + cos((3*pi)/2 - a)^2)/((pi - a)*tan(pi - a)^2)
Denominador racional [src] 
     2         2   
- cos (a) - sin (a)
-------------------
       a - pi
−sin⁡2(a)−cos⁡2(a)a−π\frac{- \sin^{2}{\left(a \right)} - \cos^{2}{\left(a \right)}}{a - \pi} 
(-cos(a)^2 - sin(a)^2)/(a - pi)
Potencias [src] 
   2         2   
cos (a) + sin (a)
-----------------
      pi - a
sin⁡2(a)+cos⁡2(a)π−a\frac{\sin^{2}{\left(a \right)} + \cos^{2}{\left(a \right)}}{\pi - a} 
                                               /                                2                                     2\
                                               |/   /    3*pi\      /     3*pi\\    /     /    3*pi\      /     3*pi\\ |
                                               || I*|a - ----|    I*|-a + ----||    |   I*|a - ----|    I*|-a + ----|| |
                2                            2 ||   \     2  /      \      2  /|    |     \     2  /      \      2  /| |
/   I*a    -I*a\  / I*(pi - a)    I*(a - pi)\  ||e               e             |    \- e             + e             / |
\- e    + e    / *\e           + e          / *||------------- + --------------|  - -----------------------------------|
                                               \\      2               2       /                     4                 /
------------------------------------------------------------------------------------------------------------------------
                                                                      2               2                                 
                                         /   I*(pi - a)    I*(a - pi)\  / I*a    -I*a\                                  
                                (pi - a)*\- e           + e          / *\e    + e    /
((ei(−a+3π2)2+ei(a−3π2)2)2−(ei(−a+3π2)−ei(a−3π2))24)(−eia+e−ia)2(ei(π−a)+ei(a−π))2(π−a)(eia+e−ia)2(−ei(π−a)+ei(a−π))2\frac{\left(\left(\frac{e^{i \left(- a + \frac{3 \pi}{2}\right)}}{2} + \frac{e^{i \left(a - \frac{3 \pi}{2}\right)}}{2}\right)^{2} - \frac{\left(e^{i \left(- a + \frac{3 \pi}{2}\right)} - e^{i \left(a - \frac{3 \pi}{2}\right)}\right)^{2}}{4}\right) \left(- e^{i a} + e^{- i a}\right)^{2} \left(e^{i \left(\pi - a\right)} + e^{i \left(a - \pi\right)}\right)^{2}}{\left(\pi - a\right) \left(e^{i a} + e^{- i a}\right)^{2} \left(- e^{i \left(\pi - a\right)} + e^{i \left(a - \pi\right)}\right)^{2}} 
(-exp(i*a) + exp(-i*a))^2*(exp(i*(pi - a)) + exp(i*(a - pi)))^2*((exp(i*(a - 3*pi/2))/2 + exp(i*(-a + 3*pi/2))/2)^2 - (-exp(i*(a - 3*pi/2)) + exp(i*(-a + 3*pi/2)))^2/4)/((pi - a)*(-exp(i*(pi - a)) + exp(i*(a - pi)))^2*(exp(i*a) + exp(-i*a))^2)
Parte trigonométrica [src] 
                                        2/a   pi\         
                                   4*cos |- - --|         
       4/a\        2/a\                  \2   4 /         
- 4*cos |-| + 4*cos |-| + --------------------------------
        \2/         \2/                     2             
                          /       2/a   pi\\              
                          |    cos |- - --||              
                          |        \2   4 /|     2/a   pi\
                          |1 + ------------| *cos |- + --|
                          |       2/a   pi\|      \2   4 /
                          |    cos |- + --||              
                          \        \2   4 //              
----------------------------------------------------------
                          pi - a
−4cos⁡4(a2)+4cos⁡2(a2)+4cos⁡2(a2−π4)(cos⁡2(a2−π4)cos⁡2(a2+π4)+1)2cos⁡2(a2+π4)π−a\frac{- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} + \frac{4 \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + 1\right)^{2} \cos^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}}{\pi - a} 
                  2        
 /         1     \     4/a\
 |1 + -----------| *sec |-|
 |       /    pi\|      \2/
 |    sec|a - --||         
 \       \    2 //         
---------------------------
                 4         
/          /a\  \          
|       sec|-|  |          
|          \2/  |          
|1 + -----------| *(pi - a)
|       /a   pi\|          
|    sec|- - --||          
\       \2   2 //
(1+1sec⁡(a−π2))2sec⁡4(a2)(π−a)(sec⁡(a2)sec⁡(a2−π2)+1)4\frac{\left(1 + \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right)^{2} \sec^{4}{\left(\frac{a}{2} \right)}}{\left(\pi - a\right) \left(\frac{\sec{\left(\frac{a}{2} \right)}}{\sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{4}} 
                  2                      
/       2/a   pi\\            2/a   pi\  
|1 - tan |- + --||       4*tan |- + --|  
\        \2   4 //             \2   4 /  
------------------- + -------------------
                  2                     2
/       2/a   pi\\    /       2/a   pi\\ 
|1 + tan |- + --||    |1 + tan |- + --|| 
\        \2   4 //    \        \2   4 // 
-----------------------------------------
                  pi - a
(1−tan⁡2(a2+π4))2(tan⁡2(a2+π4)+1)2+4tan⁡2(a2+π4)(tan⁡2(a2+π4)+1)2π−a\frac{\frac{\left(1 - \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}}{\pi - a} 
                                    2/a   pi\         
                               4*sec |- + --|         
     4         4                     \2   4 /         
- ------- + ------- + --------------------------------
     4/a\      2/a\                     2             
  sec |-|   sec |-|   /       2/a   pi\\              
      \2/       \2/   |    sec |- + --||              
                      |        \2   4 /|     2/a   pi\
                      |1 + ------------| *sec |- - --|
                      |       2/a   pi\|      \2   4 /
                      |    sec |- - --||              
                      \        \2   4 //              
------------------------------------------------------
                        pi - a
4sec⁡2(a2)−4sec⁡4(a2)+4sec⁡2(a2+π4)(1+sec⁡2(a2+π4)sec⁡2(a2−π4))2sec⁡2(a2−π4)π−a\frac{\frac{4}{\sec^{2}{\left(\frac{a}{2} \right)}} - \frac{4}{\sec^{4}{\left(\frac{a}{2} \right)}} + \frac{4 \sec^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}\right)^{2} \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}}{\pi - a} 
                  4                   2                                   
    /        2/a\\      /        2/a\\                                    
  4*|-1 + cot |-||    4*|-1 + cot |-||                                    
    \         \4//      \         \4//                   4                
- ----------------- + ----------------- + --------------------------------
                 4                   2                      2             
    /       2/a\\       /       2/a\\     /         1      \     2/a   pi\
    |1 + cot |-||       |1 + cot |-||     |1 + ------------| *cot |- + --|
    \        \4//       \        \4//     |       2/a   pi\|      \2   4 /
                                          |    cot |- + --||              
                                          \        \2   4 //              
--------------------------------------------------------------------------
                                  pi - a
−4(cot⁡2(a4)−1)4(cot⁡2(a4)+1)4+4(cot⁡2(a4)−1)2(cot⁡2(a4)+1)2+4(1+1cot⁡2(a2+π4))2cot⁡2(a2+π4)π−a\frac{- \frac{4 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4}} + \frac{4 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}} + \frac{4}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right)^{2} \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}}{\pi - a} 
                                  2  
                 /           /a\ \   
               4 |      2*tan|-| |   
  /       2/a\\  |           \2/ |   
  |1 + tan |-|| *|1 + -----------|   
  \        \4//  |           2/a\|   
                 |    1 + tan |-||   
                 \            \2//   
-------------------------------------
             4             4         
/       2/a\\  /       /a\\          
|1 - tan |-|| *|1 + tan|-|| *(pi - a)
\        \4//  \       \2//
(1+2tan⁡(a2)tan⁡2(a2)+1)2(tan⁡2(a4)+1)4(1−tan⁡2(a4))4(π−a)(tan⁡(a2)+1)4\frac{\left(1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right)^{2} \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4}}{\left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4} \left(\pi - a\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{4}} 
                          2        
         /       /    pi\\         
         |1 + cos|a - --||         
         \       \    2 //         
-----------------------------------
                 4                 
/       /a   pi\\                  
|    cos|- - --||                  
|       \2   2 /|              4/a\
|1 + -----------| *(pi - a)*cos |-|
|          /a\  |               \2/
|       cos|-|  |                  
\          \2/  /
(cos⁡(a−π2)+1)2(1+cos⁡(a2−π2)cos⁡(a2))4(π−a)cos⁡4(a2)\frac{\left(\cos{\left(a - \frac{\pi}{2} \right)} + 1\right)^{2}}{\left(1 + \frac{\cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{a}{2} \right)}}\right)^{4} \left(\pi - a\right) \cos^{4}{\left(\frac{a}{2} \right)}} 
                   2                      
/        2/a   pi\\            2/a   pi\  
|-1 + cot |- + --||       4*cot |- + --|  
\         \2   4 //             \2   4 /  
-------------------- + -------------------
                  2                      2
/       2/a   pi\\     /       2/a   pi\\ 
|1 + cot |- + --||     |1 + cot |- + --|| 
\        \2   4 //     \        \2   4 // 
------------------------------------------
                  pi - a
(cot⁡2(a2+π4)−1)2(cot⁡2(a2+π4)+1)2+4cot⁡2(a2+π4)(cot⁡2(a2+π4)+1)2π−a\frac{\frac{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{4 \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}}{\pi - a} 
   1           1      
------- + ------------
   2         2        
csc (a)   sec (pi - a)
----------------------
        pi - a
1sec⁡2(π−a)+1csc⁡2(a)π−a\frac{\frac{1}{\sec^{2}{\left(\pi - a \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}}{\pi - a} 
   1           1      
------- + ------------
   2         2/pi    \
sec (a)   sec |-- - a|
              \2     /
----------------------
        pi - a
1sec⁡2(−a+π2)+1sec⁡2(a)π−a\frac{\frac{1}{\sec^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\sec^{2}{\left(a \right)}}}{\pi - a} 
   2         2/    pi\
sin (a) + sin |a + --|
              \    2 /
----------------------
        pi - a
sin⁡2(a)+sin⁡2(a+π2)π−a\frac{\sin^{2}{\left(a \right)} + \sin^{2}{\left(a + \frac{\pi}{2} \right)}}{\pi - a} 
                                              2/  a   pi\         
                                         4*csc |- - + --|         
       4              4                        \  2   4 /         
- ------------ + ------------ + ----------------------------------
     4/pi   a\      2/pi   a\                       2             
  csc |-- - -|   csc |-- - -|   /       2/  a   pi\\              
      \2    2/       \2    2/   |    csc |- - + --||              
                                |        \  2   4 /|     2/a   pi\
                                |1 + --------------| *csc |- + --|
                                |        2/a   pi\ |      \2   4 /
                                |     csc |- + --| |              
                                \         \2   4 / /              
------------------------------------------------------------------
                              pi - a
4csc⁡2(−a2+π2)−4csc⁡4(−a2+π2)+4csc⁡2(−a2+π4)(csc⁡2(−a2+π4)csc⁡2(a2+π4)+1)2csc⁡2(a2+π4)π−a\frac{\frac{4}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - \frac{4}{\csc^{4}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + \frac{4 \csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + 1\right)^{2} \csc^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}}{\pi - a} 
                                                     2/a   pi\  
                                 4              4*tan |- + --|  
                   /        2/a\\     8/a\            \2   4 /  
2*(1 + cos(a)) - 4*|-1 + cot |-|| *sin |-| + -------------------
                   \         \4//      \4/                     2
                                             /       2/a   pi\\ 
                                             |1 + tan |- + --|| 
                                             \        \2   4 // 
----------------------------------------------------------------
                             pi - a
2(cos⁡(a)+1)−4(cot⁡2(a4)−1)4sin⁡8(a4)+4tan⁡2(a2+π4)(tan⁡2(a2+π4)+1)2π−a\frac{2 \left(\cos{\left(a \right)} + 1\right) - 4 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4} \sin^{8}{\left(\frac{a}{4} \right)} + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}}{\pi - a} 
                                  2   
                 /           /a\ \    
               4 |      2*cot|-| |    
  /       2/a\\  |           \2/ |    
  |1 + cot |-|| *|1 + -----------|    
  \        \4//  |           2/a\|    
                 |    1 + cot |-||    
                 \            \2//    
--------------------------------------
            4               4         
/      1   \  /        2/a\\          
|1 + ------| *|-1 + cot |-|| *(pi - a)
|       /a\|  \         \4//          
|    cot|-||                          
\       \2//
(1+2cot⁡(a2)cot⁡2(a2)+1)2(cot⁡2(a4)+1)4(1+1cot⁡(a2))4(π−a)(cot⁡2(a4)−1)4\frac{\left(1 + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right)^{2} \left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4}}{\left(1 + \frac{1}{\cot{\left(\frac{a}{2} \right)}}\right)^{4} \left(\pi - a\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4}} 
                        2             
            (1 + sin(a))              
--------------------------------------
               4                      
/         2/a\\                       
|    2*sin |-||                       
|          \2/|              4/pi   a\
|1 + ---------| *(pi - a)*sin |-- + -|
\      sin(a) /               \2    2/
(sin⁡(a)+1)2(π−a)(2sin⁡2(a2)sin⁡(a)+1)4sin⁡4(a2+π2)\frac{\left(\sin{\left(a \right)} + 1\right)^{2}}{\left(\pi - a\right) \left(\frac{2 \sin^{2}{\left(\frac{a}{2} \right)}}{\sin{\left(a \right)}} + 1\right)^{4} \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{2} \right)}} 
   2           4/a\        2/a\
cos (a) - 4*cos |-| + 4*cos |-|
                \2/         \2/
-------------------------------
             pi - a
−4cos⁡4(a2)+4cos⁡2(a2)+cos⁡2(a)π−a\frac{- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} + \cos^{2}{\left(a \right)}}{\pi - a} 
             2             
 /      1   \     4/pi   a\
 |1 + ------| *csc |-- - -|
 \    csc(a)/      \2    2/
---------------------------
                 4         
/       /pi   a\\          
|    csc|-- - -||          
|       \2    2/|          
|1 + -----------| *(pi - a)
|          /a\  |          
|       csc|-|  |          
\          \2/  /
(1+1csc⁡(a))2csc⁡4(−a2+π2)(1+csc⁡(−a2+π2)csc⁡(a2))4(π−a)\frac{\left(1 + \frac{1}{\csc{\left(a \right)}}\right)^{2} \csc^{4}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{a}{2} \right)}}\right)^{4} \left(\pi - a\right)} 
                                  2/a   pi\  
                             4*tan |- + --|  
       4/a\        2/a\            \2   4 /  
- 4*cos |-| + 4*cos |-| + -------------------
        \2/         \2/                     2
                          /       2/a   pi\\ 
                          |1 + tan |- + --|| 
                          \        \2   4 // 
---------------------------------------------
                    pi - a
−4cos⁡4(a2)+4cos⁡2(a2)+4tan⁡2(a2+π4)(tan⁡2(a2+π4)+1)2π−a\frac{- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}}{\pi - a} 
   1         1   
------- + -------
   2         2   
csc (a)   sec (a)
-----------------
      pi - a
1sec⁡2(a)+1csc⁡2(a)π−a\frac{\frac{1}{\sec^{2}{\left(a \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}}{\pi - a} 
                    2         
        (1 + sin(a))          
------------------------------
            4                 
/       /a\\              4/a\
|1 + tan|-|| *(pi - a)*cos |-|
\       \2//               \2/
(sin⁡(a)+1)2(π−a)(tan⁡(a2)+1)4cos⁡4(a2)\frac{\left(\sin{\left(a \right)} + 1\right)^{2}}{\left(\pi - a\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{4} \cos^{4}{\left(\frac{a}{2} \right)}} 
                            2                 
                (1 + sin(a))                  
----------------------------------------------
            4               4                 
/       /a\\  /        2/a\\              8/a\
|1 + tan|-|| *|-1 + cot |-|| *(pi - a)*sin |-|
\       \2//  \         \4//               \4/
(sin⁡(a)+1)2(π−a)(tan⁡(a2)+1)4(cot⁡2(a4)−1)4sin⁡8(a4)\frac{\left(\sin{\left(a \right)} + 1\right)^{2}}{\left(\pi - a\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{4} \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4} \sin^{8}{\left(\frac{a}{4} \right)}} 
   2         2           
cos (a) + sin (-a + 2*pi)
-------------------------
          pi - a
sin⁡2(−a+2π)+cos⁡2(a)π−a\frac{\sin^{2}{\left(- a + 2 \pi \right)} + \cos^{2}{\left(a \right)}}{\pi - a} 
                         2             
             (1 + sin(a))              
---------------------------------------
                              4        
         /      1        1   \     4/a\
(pi - a)*|1 + ------ - ------| *cos |-|
         \    sin(a)   tan(a)/      \2/
(sin⁡(a)+1)2(π−a)(1−1tan⁡(a)+1sin⁡(a))4cos⁡4(a2)\frac{\left(\sin{\left(a \right)} + 1\right)^{2}}{\left(\pi - a\right) \left(1 - \frac{1}{\tan{\left(a \right)}} + \frac{1}{\sin{\left(a \right)}}\right)^{4} \cos^{4}{\left(\frac{a}{2} \right)}} 
                                                    2/a   pi\  
                                4              4*tan |- + --|  
                   /       2/a\\     8/a\            \2   4 /  
2*(1 + cos(a)) - 4*|1 - tan |-|| *cos |-| + -------------------
                   \        \4//      \4/                     2
                                            /       2/a   pi\\ 
                                            |1 + tan |- + --|| 
                                            \        \2   4 // 
---------------------------------------------------------------
                             pi - a
−4(1−tan⁡2(a4))4cos⁡8(a4)+2(cos⁡(a)+1)+4tan⁡2(a2+π4)(tan⁡2(a2+π4)+1)2π−a\frac{- 4 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4} \cos^{8}{\left(\frac{a}{4} \right)} + 2 \left(\cos{\left(a \right)} + 1\right) + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}}{\pi - a} 
  1   
------
pi - a
1π−a\frac{1}{\pi - a} 
   2         2/    pi\
cos (a) + cos |a - --|
              \    2 /
----------------------
        pi - a
cos⁡2(a)+cos⁡2(a−π2)π−a\frac{\cos^{2}{\left(a \right)} + \cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\pi - a} 
                            2                
                (1 + sin(a))                 
---------------------------------------------
             4             4                 
/       2/a\\  /       /a\\              8/a\
|1 - tan |-|| *|1 + tan|-|| *(pi - a)*cos |-|
\        \4//  \       \2//               \4/
(sin⁡(a)+1)2(1−tan⁡2(a4))4(π−a)(tan⁡(a2)+1)4cos⁡8(a4)\frac{\left(\sin{\left(a \right)} + 1\right)^{2}}{\left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4} \left(\pi - a\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{4} \cos^{8}{\left(\frac{a}{4} \right)}} 
                                                 4/a   pi\       
                                           16*sin |- + --|       
       4/pi   a\        2/pi   a\                 \2   4 /       
- 4*sin |-- + -| + 4*sin |-- + -| + -----------------------------
        \2    2/         \2    2/                       2        
                                    /         4/a   pi\\         
                                    |    4*sin |- + --||         
                                    |          \2   4 /|     2   
                                    |1 + --------------| *cos (a)
                                    |          2       |         
                                    \       cos (a)    /         
-----------------------------------------------------------------
                              pi - a
−4sin⁡4(a2+π2)+4sin⁡2(a2+π2)+16sin⁡4(a2+π4)(4sin⁡4(a2+π4)cos⁡2(a)+1)2cos⁡2(a)π−a\frac{- 4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{2} \right)} + 4 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{2} \right)} + \frac{16 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cos^{2}{\left(a \right)}} + 1\right)^{2} \cos^{2}{\left(a \right)}}}{\pi - a} 
   2/    pi\ /   2              2   \
cos |a - --|*\cos (pi - a) + sin (a)/
    \    2 /                         
-------------------------------------
                    2/pi    \        
        (pi - a)*cos |-- - a|        
                     \2     /
(sin⁡2(a)+cos⁡2(π−a))cos⁡2(a−π2)(π−a)cos⁡2(−a+π2)\frac{\left(\sin^{2}{\left(a \right)} + \cos^{2}{\left(\pi - a \right)}\right) \cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\left(\pi - a\right) \cos^{2}{\left(- a + \frac{\pi}{2} \right)}} 
                 4                  2                      
    /       2/a\\      /       2/a\\            2/a   pi\  
  4*|1 - tan |-||    4*|1 - tan |-||       4*tan |- + --|  
    \        \4//      \        \4//             \2   4 /  
- ---------------- + ---------------- + -------------------
                4                  2                      2
   /       2/a\\      /       2/a\\     /       2/a   pi\\ 
   |1 + tan |-||      |1 + tan |-||     |1 + tan |- + --|| 
   \        \4//      \        \4//     \        \2   4 // 
-----------------------------------------------------------
                           pi - a
−4(1−tan⁡2(a4))4(tan⁡2(a4)+1)4+4(1−tan⁡2(a4))2(tan⁡2(a4)+1)2+4tan⁡2(a2+π4)(tan⁡2(a2+π4)+1)2π−a\frac{- \frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4}} + \frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}}{\pi - a} 
            2    4/a\ 
(1 + sin(a)) *sec |-| 
                  \2/ 
----------------------
            4         
/       /a\\          
|1 + tan|-|| *(pi - a)
\       \2//
(sin⁡(a)+1)2sec⁡4(a2)(π−a)(tan⁡(a2)+1)4\frac{\left(\sin{\left(a \right)} + 1\right)^{2} \sec^{4}{\left(\frac{a}{2} \right)}}{\left(\pi - a\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{4}} 
   1           1      
------- + ------------
   2         2/pi    \
csc (a)   csc |-- - a|
              \2     /
----------------------
        pi - a
1csc⁡2(−a+π2)+1csc⁡2(a)π−a\frac{\frac{1}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}}{\pi - a} 
(csc(a)^(-2) + csc(pi/2 - a)^(-2))/(pi - a)
    © Sr Examen – Калькулятор