Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ cot(-a)*sin(6*pi/5-a)*cos(pi-a)*tan(3*pi/(2+a))/(cos(pi-a)^2)

¿Cómo vas a descomponer esta cot(-a)*sin(6*pi/5-a)*cos(pi-a)*tan(3*pi/(2+a))/(cos(pi-a)^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
           /6*pi    \                / 3*pi\
cot(-a)*sin|---- - a|*cos(pi - a)*tan|-----|
           \ 5      /                \2 + a/
--------------------------------------------
                   2                        
                cos (pi - a)
sin⁡(−a+6π5)cot⁡(−a)cos⁡(π−a)tan⁡(3πa+2)cos⁡2(π−a)\frac{\sin{\left(- a + \frac{6 \pi}{5} \right)} \cot{\left(- a \right)} \cos{\left(\pi - a \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}}{\cos^{2}{\left(\pi - a \right)}} 
(((cot(-a)*sin((6*pi)/5 - a))*cos(pi - a))*tan((3*pi)/(2 + a)))/cos(pi - a)^2
Simplificación general [src] 
/               ______________\           
|              /          ___ |           
|      ___   \/  10 - 2*\/ 5  |    / 3*pi\
|1 + \/ 5  - -----------------|*tan|-----|
\                  tan(a)     /    \2 + a/
------------------------------------------
                    4
(1+5−10−25tan⁡(a))tan⁡(3πa+2)4\frac{\left(1 + \sqrt{5} - \frac{\sqrt{10 - 2 \sqrt{5}}}{\tan{\left(a \right)}}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)}}{4} 
(1 + sqrt(5) - sqrt(10 - 2*sqrt(5))/tan(a))*tan(3*pi/(2 + a))/4
Respuesta numérica [src] 
cot(-a)*sin((6*pi)/5 - a)*tan((3*pi)/(2 + a))/cos(pi - a)
cot(-a)*sin((6*pi)/5 - a)*tan((3*pi)/(2 + a))/cos(pi - a)
Denominador racional [src] 
    /    3*pi\           / 3*pi\ 
-cos|a + ----|*cot(a)*tan|-----| 
    \     10 /           \2 + a/ 
---------------------------------
              cos(a)
−cos⁡(a+3π10)tan⁡(3πa+2)cot⁡(a)cos⁡(a)- \frac{\cos{\left(a + \frac{3 \pi}{10} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}} 
-cos(a + 3*pi/10)*cot(a)*tan(3*pi/(2 + a))/cos(a)
Unión de expresiones racionales [src] 
          /-5*a + 6*pi\    / 3*pi\
cot(a)*sin|-----------|*tan|-----|
          \     5     /    \2 + a/
----------------------------------
              cos(a)
sin⁡(−5a+6π5)tan⁡(3πa+2)cot⁡(a)cos⁡(a)\frac{\sin{\left(\frac{- 5 a + 6 \pi}{5} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}} 
cot(a)*sin((-5*a + 6*pi)/5)*tan(3*pi/(2 + a))/cos(a)
Combinatoria [src] 
    /    3*pi\           / 3*pi\ 
-cos|a + ----|*cot(a)*tan|-----| 
    \     10 /           \2 + a/ 
---------------------------------
              cos(a)
−cos⁡(a+3π10)tan⁡(3πa+2)cot⁡(a)cos⁡(a)- \frac{\cos{\left(a + \frac{3 \pi}{10} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}} 
-cos(a + 3*pi/10)*cot(a)*tan(3*pi/(2 + a))/cos(a)
Denominador común [src] 
    /    3*pi\            / 3*pi\ 
-cos|a + ----|*cot(-a)*tan|-----| 
    \     10 /            \2 + a/ 
----------------------------------
           cos(pi - a)
−cos⁡(a+3π10)tan⁡(3πa+2)cot⁡(−a)cos⁡(π−a)- \frac{\cos{\left(a + \frac{3 \pi}{10} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(- a \right)}}{\cos{\left(\pi - a \right)}} 
-cos(a + 3*pi/10)*cot(-a)*tan(3*pi/(2 + a))/cos(pi - a)
Potencias [src] 
    /    3*pi\           / 3*pi\ 
-cos|a + ----|*cot(a)*tan|-----| 
    \     10 /           \2 + a/ 
---------------------------------
              cos(a)
−cos⁡(a+3π10)tan⁡(3πa+2)cot⁡(a)cos⁡(a)- \frac{\cos{\left(a + \frac{3 \pi}{10} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}} 
 /     /    6*pi\      /     6*pi\\ /   3*pi*I    -3*pi*I\        
 |   I*|a - ----|    I*|-a + ----|| |   ------    -------|        
 |     \     5  /      \      5  /| |   2 + a      2 + a |        
-\- e             + e             /*\- e       + e       /*cot(a) 
------------------------------------------------------------------
                                      / -3*pi*I    3*pi*I\        
          / I*(pi - a)    I*(a - pi)\ | -------    ------|        
          |e             e          | |  2 + a     2 + a |        
        2*|----------- + -----------|*\e        + e      /        
          \     2             2     /
−(ei(−a+6π5)−ei(a−6π5))(−e3iπa+2+e−3iπa+2)cot⁡(a)2(ei(π−a)2+ei(a−π)2)(e3iπa+2+e−3iπa+2)- \frac{\left(e^{i \left(- a + \frac{6 \pi}{5}\right)} - e^{i \left(a - \frac{6 \pi}{5}\right)}\right) \left(- e^{\frac{3 i \pi}{a + 2}} + e^{- \frac{3 i \pi}{a + 2}}\right) \cot{\left(a \right)}}{2 \left(\frac{e^{i \left(\pi - a\right)}}{2} + \frac{e^{i \left(a - \pi\right)}}{2}\right) \left(e^{\frac{3 i \pi}{a + 2}} + e^{- \frac{3 i \pi}{a + 2}}\right)} 
-(-exp(i*(a - 6*pi/5)) + exp(i*(-a + 6*pi/5)))*(-exp(3*pi*i/(2 + a)) + exp(-3*pi*i/(2 + a)))*cot(a)/(2*(exp(i*(pi - a))/2 + exp(i*(a - pi))/2)*(exp(-3*pi*i/(2 + a)) + exp(3*pi*i/(2 + a))))
Abrimos la expresión [src] 
       ___________                                      / 3*pi\     ___                  / 3*pi\
      /       ___                      cot(a)*sin(a)*tan|-----|   \/ 5 *cot(a)*sin(a)*tan|-----|
     /  5   \/ 5             / 3*pi\                    \2 + a/                          \2 + a/
-   /   - - ----- *cot(a)*tan|-----| + ------------------------ + ------------------------------
  \/    8     8              \2 + a/           4*cos(a)                      4*cos(a)
sin⁡(a)tan⁡(3πa+2)cot⁡(a)4cos⁡(a)+5sin⁡(a)tan⁡(3πa+2)cot⁡(a)4cos⁡(a)−58−58tan⁡(3πa+2)cot⁡(a)\frac{\sin{\left(a \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)}}{4 \cos{\left(a \right)}} + \frac{\sqrt{5} \sin{\left(a \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)}}{4 \cos{\left(a \right)}} - \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)} 
-sqrt(5/8 - sqrt(5)/8)*cot(a)*tan((3*pi)/(2 + a)) + cot(a)*sin(a)*tan((3*pi)/(2 + a))/(4*cos(a)) + sqrt(5)*cot(a)*sin(a)*tan((3*pi)/(2 + a))/(4*cos(a))
Compilar la expresión [src] 
           /6*pi    \    / 3*pi\
cot(-a)*sin|---- - a|*tan|-----|
           \ 5      /    \2 + a/
--------------------------------
          cos(pi - a)
sin⁡(−a+6π5)tan⁡(3πa+2)cot⁡(−a)cos⁡(π−a)\frac{\sin{\left(- a + \frac{6 \pi}{5} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(- a \right)}}{\cos{\left(\pi - a \right)}} 
cot(-a)*sin((6*pi)/5 - a)*tan((3*pi)/(2 + a))/cos(pi - a)
Parte trigonométrica [src] 
/      1   \    / 3*pi\    /a   2*pi\
|1 - ------|*tan|-----|*tan|- + ----|
\    cos(a)/    \2 + a/    \2    5  /
-------------------------------------
 /       2/a   2*pi\\    2/a\        
 |1 + tan |- + ----||*sin |-|*tan(a) 
 \        \2    5  //     \2/
(1−1cos⁡(a))tan⁡(3πa+2)tan⁡(a2+2π5)(tan⁡2(a2+2π5)+1)sin⁡2(a2)tan⁡(a)\frac{\left(1 - \frac{1}{\cos{\left(a \right)}}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \tan{\left(a \right)}} 
             / 3*pi\    
  -csc(a)*sec|-----|    
             \2 + a/    
------------------------
   / 3*pi\    /    3*pi\
csc|-----|*sec|a + ----|
   \2 + a/    \     10 /
−csc⁡(a)sec⁡(3πa+2)csc⁡(3πa+2)sec⁡(a+3π10)- \frac{\csc{\left(a \right)} \sec{\left(\frac{3 \pi}{a + 2} \right)}}{\csc{\left(\frac{3 \pi}{a + 2} \right)} \sec{\left(a + \frac{3 \pi}{10} \right)}} 
          2/a\           / 3*pi\    / 3*pi\    
     2*sec |-|*cos(a)*sec|-----|*sin|-----|    
           \2/           \2 + a/    \2 + a/    
-----------------------------------------------
/        2/a\\    /a   pi\    /a   2*pi\       
|-1 + tan |-||*sec|- - --|*sec|- + ----|*sin(a)
\         \2//    \2   10/    \2    5  /
2sin⁡(3πa+2)cos⁡(a)sec⁡2(a2)sec⁡(3πa+2)(tan⁡2(a2)−1)sin⁡(a)sec⁡(a2−π10)sec⁡(a2+2π5)\frac{2 \sin{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a \right)} \sec^{2}{\left(\frac{a}{2} \right)} \sec{\left(\frac{3 \pi}{a + 2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} - 1\right) \sin{\left(a \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{10} \right)} \sec{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}} 
   2/ 3*pi\    /    3*pi\         
sin |-----|*cos|a + ----|*sin(2*a)
    \2 + a/    \     10 /         
----------------------------------
   2       / 6*pi\    /     3*pi\ 
sin (a)*sin|-----|*sin|-a + ----| 
           \2 + a/    \      2  /
sin⁡(2a)sin⁡2(3πa+2)cos⁡(a+3π10)sin⁡2(a)sin⁡(6πa+2)sin⁡(−a+3π2)\frac{\sin{\left(2 a \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a + \frac{3 \pi}{10} \right)}}{\sin^{2}{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \sin{\left(- a + \frac{3 \pi}{2} \right)}} 
                        2/a\    / 3*pi\    /    pi\                   
                   2*sec |-|*sec|-----|*sec|a - --|                   
                         \2/    \2 + a/    \    2 /                   
----------------------------------------------------------------------
/          2/a\   \                                                   
|       sec |-|   |                                                   
|           \2/   |           /a   pi\    /a   2*pi\    /  pi    3*pi\
|-1 + ------------|*sec(a)*sec|- - --|*sec|- + ----|*sec|- -- + -----|
|        2/a   pi\|           \2   10/    \2    5  /    \  2    2 + a/
|     sec |- - --||                                                   
\         \2   2 //
2sec⁡2(a2)sec⁡(3πa+2)sec⁡(a−π2)(sec⁡2(a2)sec⁡2(a2−π2)−1)sec⁡(a)sec⁡(−π2+3πa+2)sec⁡(a2−π10)sec⁡(a2+2π5)\frac{2 \sec^{2}{\left(\frac{a}{2} \right)} \sec{\left(\frac{3 \pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - 1\right) \sec{\left(a \right)} \sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{10} \right)} \sec{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}} 
  /  1      1    \           /a   pi\    /a   2*pi\    / 3*pi\
4*|- - - --------|*cos(a)*cos|- - --|*cos|- + ----|*sin|-----|
  \  2   2*cos(a)/           \2   10/    \2    5  /    \2 + a/
--------------------------------------------------------------
                                / 3*pi\                       
                (1 + cos(a))*cos|-----|*sin(a)                
                                \2 + a/
4(−12−12cos⁡(a))sin⁡(3πa+2)cos⁡(a)cos⁡(a2−π10)cos⁡(a2+2π5)(cos⁡(a)+1)sin⁡(a)cos⁡(3πa+2)\frac{4 \left(- \frac{1}{2} - \frac{1}{2 \cos{\left(a \right)}}\right) \sin{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{10} \right)} \cos{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(\cos{\left(a \right)} + 1\right) \sin{\left(a \right)} \cos{\left(\frac{3 \pi}{a + 2} \right)}} 
   /       2/a\\    / 3*pi\    /a   2*pi\
 2*|1 + cot |-||*tan|-----|*tan|- + ----|
   \        \2//    \2 + a/    \2    5  /
-----------------------------------------
/       2/a   2*pi\\ /       2/a\\       
|1 + tan |- + ----||*|1 - cot |-||*tan(a)
\        \2    5  // \        \2//
2(cot⁡2(a2)+1)tan⁡(3πa+2)tan⁡(a2+2π5)(1−cot⁡2(a2))(tan⁡2(a2+2π5)+1)tan⁡(a)\frac{2 \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(1 - \cot^{2}{\left(\frac{a}{2} \right)}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \tan{\left(a \right)}} 
/                     ___________       \           
|      ___     ___   /       ___        |    / 3*pi\
\1 + \/ 5  - \/ 2 *\/  5 - \/ 5  *cot(a)/*tan|-----|
                                             \2 + a/
----------------------------------------------------
                         4
(−25−5cot⁡(a)+1+5)tan⁡(3πa+2)4\frac{\left(- \sqrt{2} \sqrt{5 - \sqrt{5}} \cot{\left(a \right)} + 1 + \sqrt{5}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)}}{4} 
    /     7*pi\    /  pi    3*pi\ 
-cos|-a + ----|*cos|- -- + -----| 
    \      10 /    \  2    2 + a/ 
----------------------------------
        / 3*pi\    /     pi\      
     cos|-----|*cos|-a - --|      
        \2 + a/    \     2 /
−cos⁡(−π2+3πa+2)cos⁡(−a+7π10)cos⁡(3πa+2)cos⁡(−a−π2)- \frac{\cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)} \cos{\left(- a + \frac{7 \pi}{10} \right)}}{\cos{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(- a - \frac{\pi}{2} \right)}} 
                                 2                                 
   /        _____________       \                                  
   |       /         ___     /a\|     2/a\    / 3*pi\    /a   2*pi\
-4*|-1 + \/  5 + 2*\/ 5  *tan|-|| *cos |-|*tan|-----|*tan|- + ----|
   \                         \2//      \2/    \2 + a/    \2    5  /
-------------------------------------------------------------------
                                     ___                           
                     12*sin(a) + 4*\/ 5 *sin(a)
−4(25+5tan⁡(a2)−1)2cos⁡2(a2)tan⁡(3πa+2)tan⁡(a2+2π5)45sin⁡(a)+12sin⁡(a)- \frac{4 \left(\sqrt{2 \sqrt{5} + 5} \tan{\left(\frac{a}{2} \right)} - 1\right)^{2} \cos^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{4 \sqrt{5} \sin{\left(a \right)} + 12 \sin{\left(a \right)}} 
    2/ 3*pi\             /    4*pi\ 
-sin |-----|*sin(2*a)*sin|a + ----| 
     \2 + a/             \     5  / 
------------------------------------
               2       / 6*pi\      
     cos(a)*sin (a)*sin|-----|      
                       \2 + a/
−sin⁡(2a)sin⁡2(3πa+2)sin⁡(a+4π5)sin⁡2(a)sin⁡(6πa+2)cos⁡(a)- \frac{\sin{\left(2 a \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)} \sin{\left(a + \frac{4 \pi}{5} \right)}}{\sin^{2}{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \cos{\left(a \right)}} 
            /                     ___________         \
            |              ___   /       ___          |
   2/ 3*pi\ |      ___   \/ 2 *\/  5 - \/ 5  *sin(2*a)|
sin |-----|*|1 + \/ 5  - -----------------------------|
    \2 + a/ |                           2             |
            \                      2*sin (a)          /
-------------------------------------------------------
                           / 6*pi\                     
                      2*sin|-----|                     
                           \2 + a/
(1+5−25−5sin⁡(2a)2sin⁡2(a))sin⁡2(3πa+2)2sin⁡(6πa+2)\frac{\left(1 + \sqrt{5} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)}}\right) \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)}}{2 \sin{\left(\frac{6 \pi}{a + 2} \right)}} 
        / 3*pi\    /    pi\     
     sec|-----|*sec|a - --|     
        \2 + a/    \    2 /     
--------------------------------
   /     7*pi\    /  pi    3*pi\
sec|-a + ----|*sec|- -- + -----|
   \      10 /    \  2    2 + a/
sec⁡(3πa+2)sec⁡(a−π2)sec⁡(−π2+3πa+2)sec⁡(−a+7π10)\frac{\sec{\left(\frac{3 \pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)} \sec{\left(- a + \frac{7 \pi}{10} \right)}} 
    /    3*pi\    / 3*pi\ 
-cos|a + ----|*sin|-----| 
    \     10 /    \2 + a/ 
--------------------------
       / 3*pi\            
    cos|-----|*sin(a)     
       \2 + a/
−sin⁡(3πa+2)cos⁡(a+3π10)sin⁡(a)cos⁡(3πa+2)- \frac{\sin{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a + \frac{3 \pi}{10} \right)}}{\sin{\left(a \right)} \cos{\left(\frac{3 \pi}{a + 2} \right)}} 
     2/a   2*pi\           /a   2*pi\    / 3*pi\
2*sin |- + ----|*cot(a)*cot|- + ----|*tan|-----|
      \2    5  /           \2    5  /    \2 + a/
------------------------------------------------
             /        2/a\\    2/a\             
             |-1 + tan |-||*cos |-|             
             \         \2//     \2/
2sin⁡2(a2+2π5)tan⁡(3πa+2)cot⁡(a)cot⁡(a2+2π5)(tan⁡2(a2)−1)cos⁡2(a2)\frac{2 \sin^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} - 1\right) \cos^{2}{\left(\frac{a}{2} \right)}} 
/                     ___________\           
|              ___   /       ___ |           
|      ___   \/ 2 *\/  5 - \/ 5  |    / 3*pi\
|1 + \/ 5  - --------------------|*tan|-----|
\                   tan(a)       /    \2 + a/
---------------------------------------------
                      4
(1+5−25−5tan⁡(a))tan⁡(3πa+2)4\frac{\left(1 + \sqrt{5} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{\tan{\left(a \right)}}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)}}{4} 
/                     ___________       \                  
|              ___   /       ___        |                  
|      ___   \/ 2 *\/  5 - \/ 5  *cos(a)|    /  pi    3*pi\
|1 + \/ 5  - ---------------------------|*cos|- -- + -----|
|                       /    pi\        |    \  2    2 + a/
|                    cos|a - --|        |                  
\                       \    2 /        /                  
-----------------------------------------------------------
                             / 3*pi\                       
                        4*cos|-----|                       
                             \2 + a/
(−25−5cos⁡(a)cos⁡(a−π2)+1+5)cos⁡(−π2+3πa+2)4cos⁡(3πa+2)\frac{\left(- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} + 1 + \sqrt{5}\right) \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}}{4 \cos{\left(\frac{3 \pi}{a + 2} \right)}} 
                          2/ 3*pi\    2/a   2*pi\                              
                     4*sin |-----|*sin |- + ----|*sin(2*a)                     
                           \2 + a/     \2    5  /                              
-------------------------------------------------------------------------------
/         4/a   2*pi\\                                                         
|    4*sin |- + ----|| /        2    \                                         
|          \2    5  /| |     sin (a) |    /    3*pi\    2       2/a\    / 6*pi\
|1 + ----------------|*|1 - ---------|*cos|a + ----|*sin (a)*sin |-|*sin|-----|
|        2/    3*pi\ | |         4/a\|    \     10 /             \2/    \2 + a/
|     cos |a + ----| | |    4*sin |-||                                         
\         \     10 / / \          \2//
4sin⁡(2a)sin⁡2(3πa+2)sin⁡2(a2+2π5)(1−sin⁡2(a)4sin⁡4(a2))(4sin⁡4(a2+2π5)cos⁡2(a+3π10)+1)sin⁡2(a2)sin⁡2(a)sin⁡(6πa+2)cos⁡(a+3π10)\frac{4 \sin{\left(2 a \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)} \sin^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(1 - \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \left(\frac{4 \sin^{4}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\cos^{2}{\left(a + \frac{3 \pi}{10} \right)}} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \sin^{2}{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \cos{\left(a + \frac{3 \pi}{10} \right)}} 
                     ___________       
      ___     ___   /       ___        
1 + \/ 5  - \/ 2 *\/  5 - \/ 5  *cot(a)
---------------------------------------
                   / 3*pi\             
              4*cot|-----|             
                   \2 + a/
−25−5cot⁡(a)+1+54cot⁡(3πa+2)\frac{- \sqrt{2} \sqrt{5 - \sqrt{5}} \cot{\left(a \right)} + 1 + \sqrt{5}}{4 \cot{\left(\frac{3 \pi}{a + 2} \right)}} 
                   2                               
      /       2/a\\     / 3*pi\    /a   2*pi\      
      |1 + tan |-|| *tan|-----|*tan|- + ----|      
      \        \4//     \2 + a/    \2    5  /      
---------------------------------------------------
  /       2/a   2*pi\\ /       1   \           2/a\
2*|1 + tan |- + ----||*|1 - -------|*tan(a)*tan |-|
  \        \2    5  // |       2/a\|            \4/
                       |    tan |-||               
                       \        \2//
(tan⁡2(a4)+1)2tan⁡(3πa+2)tan⁡(a2+2π5)2(1−1tan⁡2(a2))(tan⁡2(a2+2π5)+1)tan⁡2(a4)tan⁡(a)\frac{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{2 \left(1 - \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \tan^{2}{\left(\frac{a}{4} \right)} \tan{\left(a \right)}} 
             /                      ___________         \ 
             |               ___   /       ___          | 
    2/ 3*pi\ |       ___   \/ 2 *\/  5 - \/ 5  *sin(2*a)| 
-sin |-----|*|-1 - \/ 5  + -----------------------------| 
     \2 + a/ |                            2             | 
             \                       2*sin (a)          / 
----------------------------------------------------------
                            / 6*pi\                       
                       2*sin|-----|                       
                            \2 + a/
−(−5−1+25−5sin⁡(2a)2sin⁡2(a))sin⁡2(3πa+2)2sin⁡(6πa+2)- \frac{\left(- \sqrt{5} - 1 + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)}}\right) \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)}}{2 \sin{\left(\frac{6 \pi}{a + 2} \right)}} 
 /                      ___________       \ 
 |       ___     ___   /       ___        | 
-\-1 - \/ 5  + \/ 2 *\/  5 - \/ 5  *cot(a)/ 
--------------------------------------------
                     / 3*pi\                
                4*cot|-----|                
                     \2 + a/
−25−5cot⁡(a)−5−14cot⁡(3πa+2)- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \cot{\left(a \right)} - \sqrt{5} - 1}{4 \cot{\left(\frac{3 \pi}{a + 2} \right)}} 
                                      /a   pi\    /  pi    3*pi\                         
                          2*cos(a)*cos|- - --|*cos|- -- + -----|                         
                                      \2   10/    \  2    2 + a/                         
-----------------------------------------------------------------------------------------
/        2/a   pi\ \ /         2/a\   \                                                  
|     cos |- - --| | |      cos |-|   |                                                  
|         \2   10/ | |          \2/   |    / 3*pi\    /    pi\    2/a   pi\    /a   2*pi\
|1 + --------------|*|1 - ------------|*cos|-----|*cos|a - --|*cos |- - --|*cos|- + ----|
|       2/a   2*pi\| |       2/a   pi\|    \2 + a/    \    2 /     \2   2 /    \2    5  /
|    cos |- + ----|| |    cos |- - --||                                                  
\        \2    5  // \        \2   2 //
2cos⁡(a)cos⁡(−π2+3πa+2)cos⁡(a2−π10)(−cos⁡2(a2)cos⁡2(a2−π2)+1)(cos⁡2(a2−π10)cos⁡2(a2+2π5)+1)cos⁡(3πa+2)cos⁡2(a2−π2)cos⁡(a2+2π5)cos⁡(a−π2)\frac{2 \cos{\left(a \right)} \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{10} \right)}}{\left(- \frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \left(\frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{10} \right)}}{\cos^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}} + 1\right) \cos{\left(\frac{3 \pi}{a + 2} \right)} \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \cos{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} \cos{\left(a - \frac{\pi}{2} \right)}} 
            /a   pi\    /a   2*pi\    /  pi    3*pi\
2*cos(a)*cos|- - --|*cos|- + ----|*cos|- -- + -----|
            \2   10/    \2    5  /    \  2    2 + a/
----------------------------------------------------
 /        2/a   pi\\                                
 |     cos |- - --||                                
 |         \2   2 /|    2/a\    / 3*pi\    /    pi\ 
 |-1 + ------------|*cos |-|*cos|-----|*cos|a - --| 
 |          2/a\   |     \2/    \2 + a/    \    2 / 
 |       cos |-|   |                                
 \           \2/   /
2cos⁡(a)cos⁡(−π2+3πa+2)cos⁡(a2−π10)cos⁡(a2+2π5)(−1+cos⁡2(a2−π2)cos⁡2(a2))cos⁡2(a2)cos⁡(3πa+2)cos⁡(a−π2)\frac{2 \cos{\left(a \right)} \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{10} \right)} \cos{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(-1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right) \cos^{2}{\left(\frac{a}{2} \right)} \cos{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)}} 
 /                      ___________       \            
 |       ___     ___   /       ___        |    / 3*pi\ 
-\-1 - \/ 5  + \/ 2 *\/  5 - \/ 5  *cot(a)/*tan|-----| 
                                               \2 + a/ 
-------------------------------------------------------
                           4
−(25−5cot⁡(a)−5−1)tan⁡(3πa+2)4- \frac{\left(\sqrt{2} \sqrt{5 - \sqrt{5}} \cot{\left(a \right)} - \sqrt{5} - 1\right) \tan{\left(\frac{3 \pi}{a + 2} \right)}}{4} 
     2/a   pi\    4/a   pi\           /a   2*pi\    / 3*pi\
8*cot |- + --|*sin |- + --|*cot(a)*cot|- + ----|*tan|-----|
      \4   5 /     \4   5 /           \2    5  /    \2 + a/
-----------------------------------------------------------
                         2                                 
           /        2/a\\  /        2/a\\    4/a\          
           |-1 + cot |-|| *|-1 + tan |-||*sin |-|          
           \         \4//  \         \2//     \4/
8sin⁡4(a4+π5)tan⁡(3πa+2)cot⁡(a)cot⁡2(a4+π5)cot⁡(a2+2π5)(tan⁡2(a2)−1)(cot⁡2(a4)−1)2sin⁡4(a4)\frac{8 \sin^{4}{\left(\frac{a}{4} + \frac{\pi}{5} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)} \cot^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)} \cot{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{a}{4} \right)}} 
       /       1   \           /a   2*pi\     
     2*|1 + -------|*cot(a)*cot|- + ----|     
       |       2/a\|           \2    5  /     
       |    cot |-||                          
       \        \2//                          
----------------------------------------------
/       2/a   2*pi\\ /        1   \    / 3*pi\
|1 + cot |- + ----||*|-1 + -------|*cot|-----|
\        \2    5  // |        2/a\|    \2 + a/
                     |     cot |-||           
                     \         \2//
2(1+1cot⁡2(a2))cot⁡(a)cot⁡(a2+2π5)(−1+1cot⁡2(a2))(cot⁡2(a2+2π5)+1)cot⁡(3πa+2)\frac{2 \left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \cot{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(-1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \cot{\left(\frac{3 \pi}{a + 2} \right)}} 
             / 3*pi\   
  -csc(a)*sec|-----|   
             \2 + a/   
-----------------------
   / 3*pi\    /     pi\
csc|-----|*csc|-a + --|
   \2 + a/    \     5 /
−csc⁡(a)sec⁡(3πa+2)csc⁡(3πa+2)csc⁡(−a+π5)- \frac{\csc{\left(a \right)} \sec{\left(\frac{3 \pi}{a + 2} \right)}}{\csc{\left(\frac{3 \pi}{a + 2} \right)} \csc{\left(- a + \frac{\pi}{5} \right)}} 
                     2/pi   a\           /pi    3*pi\                 
                2*csc |-- - -|*csc(a)*csc|-- - -----|                 
                      \2    2/           \2    2 + a/                 
----------------------------------------------------------------------
/        2/pi   a\\                                                   
|     csc |-- - -||                                                   
|         \2    2/|    / 3*pi\    /pi    \    /a   2*pi\    /  a   pi\
|-1 + ------------|*csc|-----|*csc|-- - a|*csc|- + ----|*csc|- - + --|
|          2/a\   |    \2 + a/    \2     /    \2    5  /    \  2   10/
|       csc |-|   |                                                   
\           \2/   /
2csc⁡(a)csc⁡(π2−3πa+2)csc⁡2(−a2+π2)(−1+csc⁡2(−a2+π2)csc⁡2(a2))csc⁡(3πa+2)csc⁡(−a+π2)csc⁡(−a2+π10)csc⁡(a2+2π5)\frac{2 \csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)} \csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\left(-1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \csc{\left(\frac{3 \pi}{a + 2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{10} \right)} \csc{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}} 
      /  1      1    \                  / 3*pi\    
    4*|- - - --------|*cos(a)*csc(a)*sin|-----|    
      \  2   2*cos(a)/                  \2 + a/    
---------------------------------------------------
                / 3*pi\    /a   2*pi\    /  a   pi\
(1 + cos(a))*cos|-----|*csc|- + ----|*csc|- - + --|
                \2 + a/    \2    5  /    \  2   10/
4(−12−12cos⁡(a))sin⁡(3πa+2)cos⁡(a)csc⁡(a)(cos⁡(a)+1)cos⁡(3πa+2)csc⁡(−a2+π10)csc⁡(a2+2π5)\frac{4 \left(- \frac{1}{2} - \frac{1}{2 \cos{\left(a \right)}}\right) \sin{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a \right)} \csc{\left(a \right)}}{\left(\cos{\left(a \right)} + 1\right) \cos{\left(\frac{3 \pi}{a + 2} \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{10} \right)} \csc{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}} 
                              2                                       
                 /       2/a\\     2/a   pi\    / 3*pi\               
               8*|1 + tan |-|| *tan |- + --|*tan|-----|               
                 \        \4//      \4   5 /    \2 + a/               
----------------------------------------------------------------------
                  2              2                                    
/       2/a   pi\\  /       2/a\\  /        2/a\\           /a   2*pi\
|1 + tan |- + --|| *|1 - tan |-|| *|-1 + tan |-||*tan(a)*tan|- + ----|
\        \4   5 //  \        \4//  \         \2//           \2    5  /
8(tan⁡2(a4)+1)2tan⁡(3πa+2)tan⁡2(a4+π5)(1−tan⁡2(a4))2(tan⁡2(a2)−1)(tan⁡2(a4+π5)+1)2tan⁡(a)tan⁡(a2+2π5)\frac{8 \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)}}{\left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{2} \left(\tan^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\tan^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)} + 1\right)^{2} \tan{\left(a \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}} 
     2/a\           / 3*pi\    /a   2*pi\   
  tan |-|*cot(a)*tan|-----|*tan|- + ----|   
      \4/           \2 + a/    \2    5  /   
--------------------------------------------
  /       2/a   2*pi\\ /       2/a\\    4/a\
2*|1 + tan |- + ----||*|1 - cot |-||*sin |-|
  \        \2    5  // \        \2//     \4/
tan⁡2(a4)tan⁡(3πa+2)tan⁡(a2+2π5)cot⁡(a)2(1−cot⁡2(a2))(tan⁡2(a2+2π5)+1)sin⁡4(a4)\frac{\tan^{2}{\left(\frac{a}{4} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} \cot{\left(a \right)}}{2 \left(1 - \cot^{2}{\left(\frac{a}{2} \right)}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \sin^{4}{\left(\frac{a}{4} \right)}} 
                            2/ 3*pi\    2/a   2*pi\                                 
                       8*sin |-----|*sin |- + ----|*sin(2*a)                        
                             \2 + a/     \2    5  /                                 
------------------------------------------------------------------------------------
             /         4/a   2*pi\\                                                 
             |    4*sin |- + ----|| /        2    \                                 
             |          \2    5  /| |     sin (a) |    /    3*pi\    2       / 6*pi\
(1 - cos(a))*|1 + ----------------|*|1 - ---------|*cos|a + ----|*sin (a)*sin|-----|
             |        2/    3*pi\ | |         4/a\|    \     10 /            \2 + a/
             |     cos |a + ----| | |    4*sin |-||                                 
             \         \     10 / / \          \2//
8sin⁡(2a)sin⁡2(3πa+2)sin⁡2(a2+2π5)(1−sin⁡2(a)4sin⁡4(a2))(1−cos⁡(a))(4sin⁡4(a2+2π5)cos⁡2(a+3π10)+1)sin⁡2(a)sin⁡(6πa+2)cos⁡(a+3π10)\frac{8 \sin{\left(2 a \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)} \sin^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(1 - \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \left(1 - \cos{\left(a \right)}\right) \left(\frac{4 \sin^{4}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\cos^{2}{\left(a + \frac{3 \pi}{10} \right)}} + 1\right) \sin^{2}{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \cos{\left(a + \frac{3 \pi}{10} \right)}} 
   /       1   \    / 3*pi\    /a   2*pi\
 2*|1 + -------|*tan|-----|*tan|- + ----|
   |       2/a\|    \2 + a/    \2    5  /
   |    tan |-||                         
   \        \2//                         
-----------------------------------------
/       2/a   2*pi\\ /       1   \       
|1 + tan |- + ----||*|1 - -------|*tan(a)
\        \2    5  // |       2/a\|       
                     |    tan |-||       
                     \        \2//
2(1+1tan⁡2(a2))tan⁡(3πa+2)tan⁡(a2+2π5)(1−1tan⁡2(a2))(tan⁡2(a2+2π5)+1)tan⁡(a)\frac{2 \left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(1 - \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \tan{\left(a \right)}} 
    /      1   \    / 3*pi\    /a   2*pi\    
    |1 - ------|*tan|-----|*tan|- + ----|    
    \    cos(a)/    \2 + a/    \2    5  /    
---------------------------------------------
  /       2/a   2*pi\\    4/a\           2/a\
4*|1 + tan |- + ----||*cos |-|*tan(a)*tan |-|
  \        \2    5  //     \4/            \4/
(1−1cos⁡(a))tan⁡(3πa+2)tan⁡(a2+2π5)4(tan⁡2(a2+2π5)+1)cos⁡4(a4)tan⁡2(a4)tan⁡(a)\frac{\left(1 - \frac{1}{\cos{\left(a \right)}}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{4 \left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \cos^{4}{\left(\frac{a}{4} \right)} \tan^{2}{\left(\frac{a}{4} \right)} \tan{\left(a \right)}} 
          2/ 3*pi\    /    3*pi\                
       sin |-----|*cos|a + ----|*sin(2*a)       
           \2 + a/    \     10 /                
------------------------------------------------
/          4/a\\                                
|     4*sin |-||                                
|           \2/|    2       / 6*pi\    2/pi   a\
|-1 + ---------|*sin (a)*sin|-----|*sin |-- + -|
|         2    |            \2 + a/     \2    2/
\      sin (a) /
sin⁡(2a)sin⁡2(3πa+2)cos⁡(a+3π10)(4sin⁡4(a2)sin⁡2(a)−1)sin⁡2(a)sin⁡(6πa+2)sin⁡2(a2+π2)\frac{\sin{\left(2 a \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a + \frac{3 \pi}{10} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} - 1\right) \sin^{2}{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{2} \right)}} 
                                     2                               
                        /       2/a\\                                
                        |1 + cot |-|| *cot(a)                        
                        \        \4//                                
---------------------------------------------------------------------
  /          1       \ /       2/a\\    2/a\    / 3*pi\    /a   2*pi\
2*|1 + --------------|*|1 - cot |-||*cot |-|*cot|-----|*cot|- + ----|
  |       2/a   2*pi\| \        \2//     \4/    \2 + a/    \2    5  /
  |    cot |- + ----||                                               
  \        \2    5  //
(cot⁡2(a4)+1)2cot⁡(a)2(1−cot⁡2(a2))(1+1cot⁡2(a2+2π5))cot⁡2(a4)cot⁡(3πa+2)cot⁡(a2+2π5)\frac{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \cot{\left(a \right)}}{2 \left(1 - \cot^{2}{\left(\frac{a}{2} \right)}\right) \left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}\right) \cot^{2}{\left(\frac{a}{4} \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}} 
           2/ 3*pi\    /    3*pi\               
      2*sin |-----|*cos|a + ----|*sin(2*a)      
            \2 + a/    \     10 /               
------------------------------------------------
             /          4/a\\                   
             |     4*sin |-||                   
             |           \2/|    2       / 6*pi\
(1 + cos(a))*|-1 + ---------|*sin (a)*sin|-----|
             |         2    |            \2 + a/
             \      sin (a) /
2sin⁡(2a)sin⁡2(3πa+2)cos⁡(a+3π10)(4sin⁡4(a2)sin⁡2(a)−1)(cos⁡(a)+1)sin⁡2(a)sin⁡(6πa+2)\frac{2 \sin{\left(2 a \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a + \frac{3 \pi}{10} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} - 1\right) \left(\cos{\left(a \right)} + 1\right) \sin^{2}{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)}} 
                     2                                       
        /       2/a\\     2/a   pi\           /a   2*pi\     
      8*|1 + cot |-|| *cot |- + --|*cot(a)*cot|- + ----|     
        \        \4//      \4   5 /           \2    5  /     
-------------------------------------------------------------
                  2                              2           
/       2/a   pi\\  /        1   \ /        2/a\\     / 3*pi\
|1 + cot |- + --|| *|-1 + -------|*|-1 + cot |-|| *cot|-----|
\        \4   5 //  |        2/a\| \         \4//     \2 + a/
                    |     cot |-||                           
                    \         \2//
8(cot⁡2(a4)+1)2cot⁡(a)cot⁡2(a4+π5)cot⁡(a2+2π5)(−1+1cot⁡2(a2))(cot⁡2(a4)−1)2(cot⁡2(a4+π5)+1)2cot⁡(3πa+2)\frac{8 \left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \cot{\left(a \right)} \cot^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)} \cot{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(-1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)} + 1\right)^{2} \cot{\left(\frac{3 \pi}{a + 2} \right)}} 
                               2/a   pi\    / 3*pi\                           
                          8*tan |- + --|*tan|-----|                           
                                \4   5 /    \2 + a/                           
------------------------------------------------------------------------------
                  2              2                                            
/       2/a   pi\\  /       2/a\\  /        2/a\\    4/a\           /a   2*pi\
|1 + tan |- + --|| *|1 - tan |-|| *|-1 + tan |-||*cos |-|*tan(a)*tan|- + ----|
\        \4   5 //  \        \4//  \         \2//     \4/           \2    5  /
8tan⁡(3πa+2)tan⁡2(a4+π5)(1−tan⁡2(a4))2(tan⁡2(a2)−1)(tan⁡2(a4+π5)+1)2cos⁡4(a4)tan⁡(a)tan⁡(a2+2π5)\frac{8 \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)}}{\left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{2} \left(\tan^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\tan^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)} + 1\right)^{2} \cos^{4}{\left(\frac{a}{4} \right)} \tan{\left(a \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}} 
                 2/a   pi\    / 3*pi\    /    pi\    /a   2*pi\             
            2*sec |- - --|*sec|-----|*sec|a - --|*sec|- + ----|             
                  \2   2 /    \2 + a/    \    2 /    \2    5  /             
----------------------------------------------------------------------------
/       2/a   2*pi\\ /       2/a   pi\\                                     
|    sec |- + ----|| |    sec |- - --||                                     
|        \2    5  /| |        \2   2 /|           /a   pi\    /  pi    3*pi\
|1 + --------------|*|1 - ------------|*sec(a)*sec|- - --|*sec|- -- + -----|
|        2/a   pi\ | |         2/a\   |           \2   10/    \  2    2 + a/
|     sec |- - --| | |      sec |-|   |                                     
\         \2   10/ / \          \2/   /
2sec⁡(3πa+2)sec⁡2(a2−π2)sec⁡(a2+2π5)sec⁡(a−π2)(1−sec⁡2(a2−π2)sec⁡2(a2))(1+sec⁡2(a2+2π5)sec⁡2(a2−π10))sec⁡(a)sec⁡(−π2+3πa+2)sec⁡(a2−π10)\frac{2 \sec{\left(\frac{3 \pi}{a + 2} \right)} \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \sec{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}{\left(1 - \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right) \left(1 + \frac{\sec^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{10} \right)}}\right) \sec{\left(a \right)} \sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{10} \right)}} 
                 / 3*pi\    /a   2*pi\           
            2*tan|-----|*tan|- + ----|           
                 \2 + a/    \2    5  /           
-------------------------------------------------
/       2/a   2*pi\\ /       2/a\\    2/a\       
|1 + tan |- + ----||*|1 - cot |-||*sin |-|*tan(a)
\        \2    5  // \        \2//     \2/
2tan⁡(3πa+2)tan⁡(a2+2π5)(1−cot⁡2(a2))(tan⁡2(a2+2π5)+1)sin⁡2(a2)tan⁡(a)\frac{2 \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(1 - \cot^{2}{\left(\frac{a}{2} \right)}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \tan{\left(a \right)}} 
 /                      ___________\            
 |               ___   /       ___ |            
 |       ___   \/ 2 *\/  5 - \/ 5  |    / 3*pi\ 
-|-1 - \/ 5  + --------------------|*tan|-----| 
 \                    tan(a)       /    \2 + a/ 
------------------------------------------------
                       4
−(−5−1+25−5tan⁡(a))tan⁡(3πa+2)4- \frac{\left(- \sqrt{5} - 1 + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{\tan{\left(a \right)}}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)}}{4} 
/                     ___________       \                
|              ___   /       ___        |                
|      ___   \/ 2 *\/  5 - \/ 5  *csc(a)|    /pi    3*pi\
|1 + \/ 5  - ---------------------------|*csc|-- - -----|
|                       /pi    \        |    \2    2 + a/
|                    csc|-- - a|        |                
\                       \2     /        /                
---------------------------------------------------------
                            / 3*pi\                      
                       4*csc|-----|                      
                            \2 + a/
(−25−5csc⁡(a)csc⁡(−a+π2)+1+5)csc⁡(π2−3πa+2)4csc⁡(3πa+2)\frac{\left(- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} + 1 + \sqrt{5}\right) \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)}}{4 \csc{\left(\frac{3 \pi}{a + 2} \right)}} 
                              2                                                     
/        _____________       \                /   _____________         \           
|       /         ___     /a\|                |  /         ___       /a\|    / 3*pi\
|-1 + \/  5 + 2*\/ 5  *tan|-|| *(-1 + cos(a))*|\/  5 + 2*\/ 5   + tan|-||*tan|-----|
\                         \2//                \                      \2//    \2 + a/
------------------------------------------------------------------------------------
               /       _____________       \                                        
               |      /         ___     /a\| /      ___\           2/a\             
             2*|1 - \/  5 + 2*\/ 5  *tan|-||*\3 + \/ 5 /*sin(a)*tan |-|             
               \                        \2//                        \2/
(25+5tan⁡(a2)−1)2(cos⁡(a)−1)(tan⁡(a2)+25+5)tan⁡(3πa+2)2(5+3)(−25+5tan⁡(a2)+1)sin⁡(a)tan⁡2(a2)\frac{\left(\sqrt{2 \sqrt{5} + 5} \tan{\left(\frac{a}{2} \right)} - 1\right)^{2} \left(\cos{\left(a \right)} - 1\right) \left(\tan{\left(\frac{a}{2} \right)} + \sqrt{2 \sqrt{5} + 5}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)}}{2 \left(\sqrt{5} + 3\right) \left(- \sqrt{2 \sqrt{5} + 5} \tan{\left(\frac{a}{2} \right)} + 1\right) \sin{\left(a \right)} \tan^{2}{\left(\frac{a}{2} \right)}} 
       /       2/a\\           /a   2*pi\     
     2*|1 + tan |-||*cot(a)*cot|- + ----|     
       \        \2//           \2    5  /     
----------------------------------------------
/       2/a   2*pi\\ /        2/a\\    / 3*pi\
|1 + cot |- + ----||*|-1 + tan |-||*cot|-----|
\        \2    5  // \         \2//    \2 + a/
2(tan⁡2(a2)+1)cot⁡(a)cot⁡(a2+2π5)(tan⁡2(a2)−1)(cot⁡2(a2+2π5)+1)cot⁡(3πa+2)\frac{2 \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \cot{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \cot{\left(\frac{3 \pi}{a + 2} \right)}} 
/                     ___________            \           
|              ___   /       ___     /    pi\|           
|            \/ 2 *\/  5 - \/ 5  *sec|a - --||           
|      ___                           \    2 /|    / 3*pi\
|1 + \/ 5  - --------------------------------|*sec|-----|
\                         sec(a)             /    \2 + a/
---------------------------------------------------------
                        /  pi    3*pi\                   
                   4*sec|- -- + -----|                   
                        \  2    2 + a/
(1+5−25−5sec⁡(a−π2)sec⁡(a))sec⁡(3πa+2)4sec⁡(−π2+3πa+2)\frac{\left(1 + \sqrt{5} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}}\right) \sec{\left(\frac{3 \pi}{a + 2} \right)}}{4 \sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}} 
           /pi    3*pi\ 
-csc(a)*csc|-- - -----| 
           \2    2 + a/ 
------------------------
   / 3*pi\    /    3*pi\
csc|-----|*sec|a + ----|
   \2 + a/    \     10 /
−csc⁡(a)csc⁡(π2−3πa+2)csc⁡(3πa+2)sec⁡(a+3π10)- \frac{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)}}{\csc{\left(\frac{3 \pi}{a + 2} \right)} \sec{\left(a + \frac{3 \pi}{10} \right)}} 
 /                      ___________       \                 
 |               ___   /       ___        |                 
 |       ___   \/ 2 *\/  5 - \/ 5  *csc(a)|    /pi    3*pi\ 
-|-1 - \/ 5  + ---------------------------|*csc|-- - -----| 
 |                        /pi    \        |    \2    2 + a/ 
 |                     csc|-- - a|        |                 
 \                        \2     /        /                 
------------------------------------------------------------
                             / 3*pi\                        
                        4*csc|-----|                        
                             \2 + a/
−(25−5csc⁡(a)csc⁡(−a+π2)−5−1)csc⁡(π2−3πa+2)4csc⁡(3πa+2)- \frac{\left(\frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} - \sqrt{5} - 1\right) \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)}}{4 \csc{\left(\frac{3 \pi}{a + 2} \right)}} 
 /                      ___________            \            
 |               ___   /       ___     /    pi\|            
 |             \/ 2 *\/  5 - \/ 5  *sec|a - --||            
 |       ___                           \    2 /|    / 3*pi\ 
-|-1 - \/ 5  + --------------------------------|*sec|-----| 
 \                          sec(a)             /    \2 + a/ 
------------------------------------------------------------
                         /  pi    3*pi\                     
                    4*sec|- -- + -----|                     
                         \  2    2 + a/
−(−5−1+25−5sec⁡(a−π2)sec⁡(a))sec⁡(3πa+2)4sec⁡(−π2+3πa+2)- \frac{\left(- \sqrt{5} - 1 + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}}\right) \sec{\left(\frac{3 \pi}{a + 2} \right)}}{4 \sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}} 
                    2/a\           /pi    3*pi\    /  a   pi\               
               2*csc |-|*csc(a)*csc|-- - -----|*csc|- - + --|               
                     \2/           \2    2 + a/    \  2   10/               
----------------------------------------------------------------------------
/       2/  a   pi\\ /         2/a\   \                                     
|    csc |- - + --|| |      csc |-|   |                                     
|        \  2   10/| |          \2/   |    / 3*pi\    /pi    \    /a   2*pi\
|1 + --------------|*|1 - ------------|*csc|-----|*csc|-- - a|*csc|- + ----|
|       2/a   2*pi\| |       2/pi   a\|    \2 + a/    \2     /    \2    5  /
|    csc |- + ----|| |    csc |-- - -||                                     
\        \2    5  // \        \2    2//
2csc⁡2(a2)csc⁡(a)csc⁡(π2−3πa+2)csc⁡(−a2+π10)(−csc⁡2(a2)csc⁡2(−a2+π2)+1)(csc⁡2(−a2+π10)csc⁡2(a2+2π5)+1)csc⁡(3πa+2)csc⁡(−a+π2)csc⁡(a2+2π5)\frac{2 \csc^{2}{\left(\frac{a}{2} \right)} \csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{10} \right)}}{\left(- \frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1\right) \left(\frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{10} \right)}}{\csc^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}} + 1\right) \csc{\left(\frac{3 \pi}{a + 2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)} \csc{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}} 
 /                      ___________       \                   
 |               ___   /       ___        |                   
 |       ___   \/ 2 *\/  5 - \/ 5  *cos(a)|    /  pi    3*pi\ 
-|-1 - \/ 5  + ---------------------------|*cos|- -- + -----| 
 |                        /    pi\        |    \  2    2 + a/ 
 |                     cos|a - --|        |                   
 \                        \    2 /        /                   
--------------------------------------------------------------
                              / 3*pi\                         
                         4*cos|-----|                         
                              \2 + a/
−(25−5cos⁡(a)cos⁡(a−π2)−5−1)cos⁡(−π2+3πa+2)4cos⁡(3πa+2)- \frac{\left(\frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} - \sqrt{5} - 1\right) \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}}{4 \cos{\left(\frac{3 \pi}{a + 2} \right)}} 
-(-1 - sqrt(5) + sqrt(2)*sqrt(5 - sqrt(5))*cos(a)/cos(a - pi/2))*cos(-pi/2 + 3*pi/(2 + a))/(4*cos(3*pi/(2 + a)))
    © Sr Examen – Калькулятор