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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   2       -1       /  pi \    / 3*pi\       
sin (a) - ------*cos|-----|*cot|-----|*sin(a)
          tan(2)    \2 + a/    \2 + a/
$$- \cos{\left(\frac{\pi}{a + 2} \right)} \left(- \frac{1}{\tan{\left(2 \right)}}\right) \cot{\left(\frac{3 \pi}{a + 2} \right)} \sin{\left(a \right)} + \sin^{2}{\left(a \right)}$$ 
sin(a)^2 - ((-1/tan(2))*cos(pi/(2 + a)))*cot((3*pi)/(2 + a))*sin(a)
Simplificación general [src] 
/       /  pi \            \       
|    cos|-----|            |       
|       \2 + a/            |       
|----------------- + sin(a)|*sin(a)
|          / 3*pi\         |       
|tan(2)*tan|-----|         |       
\          \2 + a/         /
$$\left(\sin{\left(a \right)} + \frac{\cos{\left(\frac{\pi}{a + 2} \right)}}{\tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}}\right) \sin{\left(a \right)}$$ 
(cos(pi/(2 + a))/(tan(2)*tan(3*pi/(2 + a))) + sin(a))*sin(a)
Denominador racional [src] 
   2                /  pi \    / 3*pi\       
sin (a)*tan(2) + cos|-----|*cot|-----|*sin(a)
                    \2 + a/    \2 + a/       
---------------------------------------------
                    tan(2)
$$\frac{\sin^{2}{\left(a \right)} \tan{\left(2 \right)} + \sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)}}{\tan{\left(2 \right)}}$$ 
(sin(a)^2*tan(2) + cos(pi/(2 + a))*cot(3*pi/(2 + a))*sin(a))/tan(2)
Denominador común [src] 
             /  pi \    / 3*pi\       
          cos|-----|*cot|-----|*sin(a)
   2         \2 + a/    \2 + a/       
sin (a) + ----------------------------
                     tan(2)
$$\sin^{2}{\left(a \right)} + \frac{\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)}}{\tan{\left(2 \right)}}$$ 
sin(a)^2 + cos(pi/(2 + a))*cot(3*pi/(2 + a))*sin(a)/tan(2)
Combinatoria [src] 
/   /  pi \    / 3*pi\                \       
|cos|-----|*cot|-----| + sin(a)*tan(2)|*sin(a)
\   \2 + a/    \2 + a/                /       
----------------------------------------------
                    tan(2)
$$\frac{\left(\sin{\left(a \right)} \tan{\left(2 \right)} + \cos{\left(\frac{\pi}{a + 2} \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)}\right) \sin{\left(a \right)}}{\tan{\left(2 \right)}}$$ 
(cos(pi/(2 + a))*cot(3*pi/(2 + a)) + sin(a)*tan(2))*sin(a)/tan(2)
Potencias [src] 
                      /  pi*I    -pi*I \                                           
                      | -----    ------|                                           
                      | 2 + a    2 + a |                                           
                  2   |e        e      | /   -I*a    I*a\ / -2*I    2*I\    / 3*pi\
  /   -I*a    I*a\    |------ + -------|*\- e     + e   /*\e     + e   /*cot|-----|
  \- e     + e   /    \  2         2   /                                    \2 + a/
- ----------------- - -------------------------------------------------------------
          4                                   /   2*I    -2*I\                     
                                            2*\- e    + e    /
$$- \frac{\left(e^{i a} - e^{- i a}\right)^{2}}{4} - \frac{\left(e^{- 2 i} + e^{2 i}\right) \left(e^{i a} - e^{- i a}\right) \left(\frac{e^{\frac{i \pi}{a + 2}}}{2} + \frac{e^{- \frac{i \pi}{a + 2}}}{2}\right) \cot{\left(\frac{3 \pi}{a + 2} \right)}}{2 \left(e^{- 2 i} - e^{2 i}\right)}$$ 
             /  pi \    / 3*pi\       
          cos|-----|*cot|-----|*sin(a)
   2         \2 + a/    \2 + a/       
sin (a) + ----------------------------
                     tan(2)
$$\sin^{2}{\left(a \right)} + \frac{\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)}}{\tan{\left(2 \right)}}$$ 
sin(a)^2 + cos(pi/(2 + a))*cot(3*pi/(2 + a))*sin(a)/tan(2)
Compilar la expresión [src] 
             /  pi \    / 3*pi\       
          cos|-----|*cot|-----|*sin(a)
   2         \2 + a/    \2 + a/       
sin (a) + ----------------------------
                     tan(2)
$$\sin^{2}{\left(a \right)} + \frac{\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)}}{\tan{\left(2 \right)}}$$ 
sin(a)^2 + cos(pi/(2 + a))*cot((3*pi)/(2 + a))*sin(a)/tan(2)
Abrimos la expresión [src] 
             /  pi \    / 3*pi\             /  pi \    / 3*pi\              
          cos|-----|*cot|-----|*sin(a)   cos|-----|*cot|-----|*sin(a)*tan(1)
   2         \2 + a/    \2 + a/             \2 + a/    \2 + a/              
sin (a) + ---------------------------- - -----------------------------------
                    2*tan(1)                              2
$$\sin^{2}{\left(a \right)} - \frac{\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} \tan{\left(1 \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)}}{2} + \frac{\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)}}{2 \tan{\left(1 \right)}}$$ 
sin(a)^2 + cos(pi/(2 + a))*cot((3*pi)/(2 + a))*sin(a)/(2*tan(1)) - cos(pi/(2 + a))*cot((3*pi)/(2 + a))*sin(a)*tan(1)/2
Unión de expresiones racionales [src] 
/   /  pi \    / 3*pi\                \       
|cos|-----|*cot|-----| + sin(a)*tan(2)|*sin(a)
\   \2 + a/    \2 + a/                /       
----------------------------------------------
                    tan(2)
$$\frac{\left(\sin{\left(a \right)} \tan{\left(2 \right)} + \cos{\left(\frac{\pi}{a + 2} \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)}\right) \sin{\left(a \right)}}{\tan{\left(2 \right)}}$$ 
(cos(pi/(2 + a))*cot(3*pi/(2 + a)) + sin(a)*tan(2))*sin(a)/tan(2)
Respuesta numérica [src] 
sin(a)^2 - 0.457657554360286*cos(pi/(2 + a))*cot((3*pi)/(2 + a))*sin(a)
sin(a)^2 - 0.457657554360286*cos(pi/(2 + a))*cot((3*pi)/(2 + a))*sin(a)
Parte trigonométrica [src] 
                   /      2      \       / 2           \
                   |pi + a  + 2*a|       |a  - pi + 2*a|
                sin|-------------|    sin|-------------|
1   cos(2*a)       \    2 + a    /       \    2 + a    /
- - -------- + ------------------- + -------------------
2      2                   / 3*pi\               / 3*pi\
               2*tan(2)*tan|-----|   2*tan(2)*tan|-----|
                           \2 + a/               \2 + a/
$$\frac{\sin{\left(\frac{a^{2} + 2 a - \pi}{a + 2} \right)}}{2 \tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}} + \frac{\sin{\left(\frac{a^{2} + 2 a + \pi}{a + 2} \right)}}{2 \tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}} - \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2}$$ 
          /       /  pi \            \       
          |    cos|-----|            |       
     2/a\ |       \2 + a/            |    /a\
2*sin |-|*|----------------- + sin(a)|*cot|-|
      \2/ |          / 3*pi\         |    \2/
          |tan(2)*tan|-----|         |       
          \          \2 + a/         /
$$2 \left(\sin{\left(a \right)} + \frac{\cos{\left(\frac{\pi}{a + 2} \right)}}{\tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}}\right) \sin^{2}{\left(\frac{a}{2} \right)} \cot{\left(\frac{a}{2} \right)}$$ 
       2/a\                    /       2/    pi   \\    /a\           
  4*tan |-|                  2*|1 - tan |---------||*tan|-|           
        \2/                    \        \2*(2 + a)//    \2/           
-------------- + -----------------------------------------------------
             2   /       2/a\\ /       2/    pi   \\           / 3*pi\
/       2/a\\    |1 + tan |-||*|1 + tan |---------||*tan(2)*tan|-----|
|1 + tan |-||    \        \2// \        \2*(2 + a)//           \2 + a/
\        \2//
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right) \tan{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}} + \frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}$$ 
                                / 3*pi\              
                      csc(2)*csc|-----|              
  1                             \2 + a/              
------ + --------------------------------------------
csc(a)      /     pi\    /pi     pi \    /pi    3*pi\
         csc|-2 + --|*csc|-- - -----|*csc|-- - -----|
            \     2 /    \2    2 + a/    \2    2 + a/
-----------------------------------------------------
                        csc(a)
$$\frac{\frac{\csc{\left(2 \right)} \csc{\left(\frac{3 \pi}{a + 2} \right)}}{\csc{\left(-2 + \frac{\pi}{2} \right)} \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 2} \right)}} + \frac{1}{\csc{\left(a \right)}}}{\csc{\left(a \right)}}$$ 
                               /a       pi   \                               /a       pi   \            
                            tan|- + ---------|                            tan|- - ---------|            
1   cos(2*a)                   \2   2*(2 + a)/                               \2   2*(2 + a)/            
- - -------- + ------------------------------------------- + -------------------------------------------
2      2       /       2/a       pi   \\           / 3*pi\   /       2/a       pi   \\           / 3*pi\
               |1 + tan |- + ---------||*tan(2)*tan|-----|   |1 + tan |- - ---------||*tan(2)*tan|-----|
               \        \2   2*(2 + a)//           \2 + a/   \        \2   2*(2 + a)//           \2 + a/
$$- \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2} + \frac{\tan{\left(\frac{a}{2} + \frac{\pi}{2 \left(a + 2\right)} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}} + \frac{\tan{\left(\frac{a}{2} - \frac{\pi}{2 \left(a + 2\right)} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} - \frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}}$$ 
                       /    pi\    /  pi    3*pi\      
                    sec|2 - --|*sec|- -- + -----|      
     1                 \    2 /    \  2    2 + a/      
------------ + ----------------------------------------
   2/    pi\             /  pi \    / 3*pi\    /    pi\
sec |a - --|   sec(2)*sec|-----|*sec|-----|*sec|a - --|
    \    2 /             \2 + a/    \2 + a/    \    2 /
$$\frac{1}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} + \frac{\sec{\left(2 - \frac{\pi}{2} \right)} \sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}}{\sec{\left(2 \right)} \sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(\frac{3 \pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}$$ 
       2/a\        /        2/    pi   \\           /a\    / 3*pi\
  4*cot |-|      2*|-1 + cot |---------||*cot(2)*cot|-|*cot|-----|
        \2/        \         \2*(2 + a)//           \2/    \2 + a/
-------------- + -------------------------------------------------
             2          /       2/a\\ /       2/    pi   \\       
/       2/a\\           |1 + cot |-||*|1 + cot |---------||       
|1 + cot |-||           \        \2// \        \2*(2 + a)//       
\        \2//
$$\frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \cot{\left(2 \right)} \cot{\left(\frac{a}{2} \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right)} + \frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}$$ 
                         /  pi \    / 3*pi\    /    pi\
               cos(2)*cos|-----|*cos|-----|*cos|a - --|
   2/    pi\             \2 + a/    \2 + a/    \    2 /
cos |a - --| + ----------------------------------------
    \    2 /           /    pi\    /  pi    3*pi\      
                    cos|2 - --|*cos|- -- + -----|      
                       \    2 /    \  2    2 + a/
$$\frac{\cos{\left(2 \right)} \cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{\cos{\left(2 - \frac{\pi}{2} \right)} \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}} + \cos^{2}{\left(a - \frac{\pi}{2} \right)}$$ 
                     /      pi \           /      pi \  
                  sin|a + -----|        sin|a - -----|  
1   cos(2*a)         \    2 + a/           \    2 + a/  
- - -------- + ------------------- + -------------------
2      2                   / 3*pi\               / 3*pi\
               2*tan(2)*tan|-----|   2*tan(2)*tan|-----|
                           \2 + a/               \2 + a/
$$\frac{\sin{\left(a - \frac{\pi}{a + 2} \right)}}{2 \tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}} + \frac{\sin{\left(a + \frac{\pi}{a + 2} \right)}}{2 \tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}} - \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2}$$ 
                                     / 3*pi\                 
                           csc(2)*csc|-----|                 
   1                                 \2 + a/                 
------- + ---------------------------------------------------
   2                /     pi\    /pi     pi \    /pi    3*pi\
csc (a)   csc(a)*csc|-2 + --|*csc|-- - -----|*csc|-- - -----|
                    \     2 /    \2    2 + a/    \2    2 + a/
$$\frac{\csc{\left(2 \right)} \csc{\left(\frac{3 \pi}{a + 2} \right)}}{\csc{\left(a \right)} \csc{\left(-2 + \frac{\pi}{2} \right)} \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 2} \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}$$ 
                                              / 3*pi\                                         / 3*pi\              
                                    csc(2)*csc|-----|                               csc(2)*csc|-----|              
1          1                                  \2 + a/                                         \2 + a/              
- - --------------- + --------------------------------------------- + ---------------------------------------------
2        /pi      \        /     pi\    /      pi \    /pi    3*pi\        /     pi\    /      pi \    /pi    3*pi\
    2*csc|-- - 2*a|   2*csc|-2 + --|*csc|a + -----|*csc|-- - -----|   2*csc|-2 + --|*csc|a - -----|*csc|-- - -----|
         \2       /        \     2 /    \    2 + a/    \2    2 + a/        \     2 /    \    2 + a/    \2    2 + a/
$$\frac{\csc{\left(2 \right)} \csc{\left(\frac{3 \pi}{a + 2} \right)}}{2 \csc{\left(-2 + \frac{\pi}{2} \right)} \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)} \csc{\left(a + \frac{\pi}{a + 2} \right)}} + \frac{\csc{\left(2 \right)} \csc{\left(\frac{3 \pi}{a + 2} \right)}}{2 \csc{\left(-2 + \frac{\pi}{2} \right)} \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)} \csc{\left(a - \frac{\pi}{a + 2} \right)}} + \frac{1}{2} - \frac{1}{2 \csc{\left(- 2 a + \frac{\pi}{2} \right)}}$$ 
                    /  pi \    / 3*pi\       
          cos(2)*cos|-----|*cos|-----|*sin(a)
   2                \2 + a/    \2 + a/       
sin (a) + -----------------------------------
                             / 3*pi\         
                   sin(2)*sin|-----|         
                             \2 + a/
$$\sin^{2}{\left(a \right)} + \frac{\sin{\left(a \right)} \cos{\left(2 \right)} \cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(\frac{3 \pi}{a + 2} \right)}}{\sin{\left(2 \right)} \sin{\left(\frac{3 \pi}{a + 2} \right)}}$$ 
          /       /  pi \            \       
          |    cos|-----|            |       
     2/a\ |       \2 + a/            |    /a\
2*cos |-|*|----------------- + sin(a)|*tan|-|
      \2/ |          / 3*pi\         |    \2/
          |tan(2)*tan|-----|         |       
          \          \2 + a/         /
$$2 \left(\sin{\left(a \right)} + \frac{\cos{\left(\frac{\pi}{a + 2} \right)}}{\tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}}\right) \cos^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{a}{2} \right)}$$ 
                 /    pi\    /  pi    3*pi\
              sec|2 - --|*sec|- -- + -----|
     1           \    2 /    \  2    2 + a/
----------- + -----------------------------
   /    pi\              /  pi \    / 3*pi\
sec|a - --|    sec(2)*sec|-----|*sec|-----|
   \    2 /              \2 + a/    \2 + a/
-------------------------------------------
                   /    pi\                
                sec|a - --|                
                   \    2 /
$$\frac{\frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} + \frac{\sec{\left(2 - \frac{\pi}{2} \right)} \sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}}{\sec{\left(2 \right)} \sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(\frac{3 \pi}{a + 2} \right)}}}{\sec{\left(a - \frac{\pi}{2} \right)}}$$ 
/           /  pi \    / 3*pi\              \            
| cos(2)*cos|-----|*cos|-----|              |            
|           \2 + a/    \2 + a/      /    pi\|    /    pi\
|----------------------------- + cos|a - --||*cos|a - --|
|   /    pi\    /  pi    3*pi\      \    2 /|    \    2 /
|cos|2 - --|*cos|- -- + -----|              |            
\   \    2 /    \  2    2 + a/              /
$$\left(\frac{\cos{\left(2 \right)} \cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(\frac{3 \pi}{a + 2} \right)}}{\cos{\left(2 - \frac{\pi}{2} \right)} \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}} + \cos{\left(a - \frac{\pi}{2} \right)}\right) \cos{\left(a - \frac{\pi}{2} \right)}$$ 
             /  pi \                  / 6*pi\
          cos|-----|*sin(4)*sin(a)*sin|-----|
   2         \2 + a/                  \2 + a/
sin (a) + -----------------------------------
                      2       2/ 3*pi\       
                 4*sin (2)*sin |-----|       
                               \2 + a/
$$\sin^{2}{\left(a \right)} + \frac{\sin{\left(4 \right)} \sin{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \cos{\left(\frac{\pi}{a + 2} \right)}}{4 \sin^{2}{\left(2 \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)}}$$ 
                             / 3*pi\         
                   csc(2)*csc|-----|         
   1                         \2 + a/         
------- + -----------------------------------
   2                       /  pi \    / 3*pi\
csc (a)   csc(a)*sec(2)*sec|-----|*sec|-----|
                           \2 + a/    \2 + a/
$$\frac{\csc{\left(2 \right)} \csc{\left(\frac{3 \pi}{a + 2} \right)}}{\csc{\left(a \right)} \sec{\left(2 \right)} \sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(\frac{3 \pi}{a + 2} \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}$$ 
  /       /a\                     2/    pi   \          \       
  |  2*tan|-|              1 - tan |---------|          |       
  |       \2/                      \2*(2 + a)/          |    /a\
2*|----------- + ---------------------------------------|*tan|-|
  |       2/a\   /       2/    pi   \\           / 3*pi\|    \2/
  |1 + tan |-|   |1 + tan |---------||*tan(2)*tan|-----||       
  \        \2/   \        \2*(2 + a)//           \2 + a//       
----------------------------------------------------------------
                                 2/a\                           
                          1 + tan |-|                           
                                  \2/
$$\frac{2 \left(\frac{1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}}{\left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}} + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}$$ 
       /pi      \             / 6*pi\    /      pi \             / 6*pi\    /      pi \
    sin|-- + 2*a|   sin(4)*sin|-----|*sin|a + -----|   sin(4)*sin|-----|*sin|a - -----|
1      \2       /             \2 + a/    \    2 + a/             \2 + a/    \    2 + a/
- - ------------- + -------------------------------- + --------------------------------
2         2                   2       2/ 3*pi\                   2       2/ 3*pi\      
                         8*sin (2)*sin |-----|              8*sin (2)*sin |-----|      
                                       \2 + a/                            \2 + a/
$$- \frac{\sin{\left(2 a + \frac{\pi}{2} \right)}}{2} + \frac{1}{2} + \frac{\sin{\left(4 \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \sin{\left(a - \frac{\pi}{a + 2} \right)}}{8 \sin^{2}{\left(2 \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)}} + \frac{\sin{\left(4 \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \sin{\left(a + \frac{\pi}{a + 2} \right)}}{8 \sin^{2}{\left(2 \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)}}$$ 
                         /    pi\    /  pi    3*pi\                /    pi\    /  pi    3*pi\     
                      sec|2 - --|*sec|- -- + -----|             sec|2 - --|*sec|- -- + -----|     
1       1                \    2 /    \  2    2 + a/                \    2 /    \  2    2 + a/     
- - ---------- + --------------------------------------- + ---------------------------------------
2   2*sec(2*a)               / 3*pi\    /    pi     pi \               / 3*pi\    /    pi     pi \
                 2*sec(2)*sec|-----|*sec|a - -- + -----|   2*sec(2)*sec|-----|*sec|a - -- - -----|
                             \2 + a/    \    2    2 + a/               \2 + a/    \    2    2 + a/
$$\frac{1}{2} + \frac{\sec{\left(2 - \frac{\pi}{2} \right)} \sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}}{2 \sec{\left(2 \right)} \sec{\left(\frac{3 \pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} + \frac{\pi}{a + 2} \right)}} + \frac{\sec{\left(2 - \frac{\pi}{2} \right)} \sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}}{2 \sec{\left(2 \right)} \sec{\left(\frac{3 \pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} - \frac{\pi}{a + 2} \right)}} - \frac{1}{2 \sec{\left(2 a \right)}}$$ 
                         / 3*pi\    /    pi     pi \             / 3*pi\    /    pi     pi \
               cos(2)*cos|-----|*cos|a - -- + -----|   cos(2)*cos|-----|*cos|a - -- - -----|
1   cos(2*a)             \2 + a/    \    2    2 + a/             \2 + a/    \    2    2 + a/
- - -------- + ------------------------------------- + -------------------------------------
2      2               /    pi\    /  pi    3*pi\              /    pi\    /  pi    3*pi\   
                  2*cos|2 - --|*cos|- -- + -----|         2*cos|2 - --|*cos|- -- + -----|   
                       \    2 /    \  2    2 + a/              \    2 /    \  2    2 + a/
$$- \frac{\cos{\left(2 a \right)}}{2} + \frac{\cos{\left(2 \right)} \cos{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} - \frac{\pi}{a + 2} \right)}}{2 \cos{\left(2 - \frac{\pi}{2} \right)} \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}} + \frac{\cos{\left(2 \right)} \cos{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} + \frac{\pi}{a + 2} \right)}}{2 \cos{\left(2 - \frac{\pi}{2} \right)} \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}} + \frac{1}{2}$$ 
/       /  pi \            \       
|    cos|-----|            |       
|       \2 + a/            |       
|----------------- + sin(a)|*sin(a)
|          / 3*pi\         |       
|tan(2)*tan|-----|         |       
\          \2 + a/         /
$$\left(\sin{\left(a \right)} + \frac{\cos{\left(\frac{\pi}{a + 2} \right)}}{\tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}}\right) \sin{\left(a \right)}$$ 
                           / 6*pi\    /pi     pi \
          sin(4)*sin(a)*sin|-----|*sin|-- + -----|
   2                       \2 + a/    \2    2 + a/
sin (a) + ----------------------------------------
                        2       2/ 3*pi\          
                   4*sin (2)*sin |-----|          
                                 \2 + a/
$$\sin^{2}{\left(a \right)} + \frac{\sin{\left(4 \right)} \sin{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)}}{4 \sin^{2}{\left(2 \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)}}$$ 
/          / 6*pi\    /pi     pi \         \       
|sin(4)*sin|-----|*sin|-- + -----|         |       
|          \2 + a/    \2    2 + a/         |       
|--------------------------------- + sin(a)|*sin(a)
|           2       2/ 3*pi\               |       
|      4*sin (2)*sin |-----|               |       
\                    \2 + a/               /
$$\left(\sin{\left(a \right)} + \frac{\sin{\left(4 \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)}}{4 \sin^{2}{\left(2 \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)}}\right) \sin{\left(a \right)}$$ 
                                      /a       pi   \                               /a       pi   \            
             2                     tan|- + ---------|                            tan|- - ---------|            
1     1 - tan (a)                     \2   2*(2 + a)/                               \2   2*(2 + a)/            
- - --------------- + ------------------------------------------- + -------------------------------------------
2     /       2   \   /       2/a       pi   \\           / 3*pi\   /       2/a       pi   \\           / 3*pi\
    2*\1 + tan (a)/   |1 + tan |- + ---------||*tan(2)*tan|-----|   |1 + tan |- - ---------||*tan(2)*tan|-----|
                      \        \2   2*(2 + a)//           \2 + a/   \        \2   2*(2 + a)//           \2 + a/
$$- \frac{1 - \tan^{2}{\left(a \right)}}{2 \left(\tan^{2}{\left(a \right)} + 1\right)} + \frac{1}{2} + \frac{\tan{\left(\frac{a}{2} + \frac{\pi}{2 \left(a + 2\right)} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}} + \frac{\tan{\left(\frac{a}{2} - \frac{\pi}{2 \left(a + 2\right)} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} - \frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \tan{\left(2 \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}}$$ 
  /       /a\    /        2/    pi   \\           / 3*pi\\       
  |  2*cot|-|    |-1 + cot |---------||*cot(2)*cot|-----||       
  |       \2/    \         \2*(2 + a)//           \2 + a/|    /a\
2*|----------- + ----------------------------------------|*cot|-|
  |       2/a\                    2/    pi   \           |    \2/
  |1 + cot |-|             1 + cot |---------|           |       
  \        \2/                     \2*(2 + a)/           /       
-----------------------------------------------------------------
                                  2/a\                           
                           1 + cot |-|                           
                                   \2/
$$\frac{2 \left(\frac{\left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \cot{\left(2 \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)}}{\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1} + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}$$ 
                                / 3*pi\    /a       pi   \             / 3*pi\    /a       pi   \
              2       cot(2)*cot|-----|*cot|- + ---------|   cot(2)*cot|-----|*cot|- - ---------|
1     -1 + cot (a)              \2 + a/    \2   2*(2 + a)/             \2 + a/    \2   2*(2 + a)/
- - --------------- + ------------------------------------ + ------------------------------------
2     /       2   \                2/a       pi   \                       2/a       pi   \       
    2*\1 + cot (a)/         1 + cot |- + ---------|                1 + cot |- - ---------|       
                                    \2   2*(2 + a)/                        \2   2*(2 + a)/
$$- \frac{\cot^{2}{\left(a \right)} - 1}{2 \left(\cot^{2}{\left(a \right)} + 1\right)} + \frac{1}{2} + \frac{\cot{\left(2 \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(\frac{a}{2} + \frac{\pi}{2 \left(a + 2\right)} \right)}}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{2 \left(a + 2\right)} \right)} + 1} + \frac{\cot{\left(2 \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(\frac{a}{2} - \frac{\pi}{2 \left(a + 2\right)} \right)}}{\cot^{2}{\left(\frac{a}{2} - \frac{\pi}{2 \left(a + 2\right)} \right)} + 1}$$ 
1/2 - (-1 + cot(a)^2)/(2*(1 + cot(a)^2)) + cot(2)*cot(3*pi/(2 + a))*cot(a/2 + pi/(2*(2 + a)))/(1 + cot(a/2 + pi/(2*(2 + a)))^2) + cot(2)*cot(3*pi/(2 + a))*cot(a/2 - pi/(2*(2 + a)))/(1 + cot(a/2 - pi/(2*(2 + a)))^2)
    © Sr Examen – Калькулятор