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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(16*pi/5)*tan(pi+a)-cos(pi/(2+a))*sin(pi+a)

¿Cómo vas a descomponer esta tan(16*pi/5)*tan(pi+a)-cos(pi/(2+a))*sin(pi+a) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /16*pi\                  /  pi \            
tan|-----|*tan(pi + a) - cos|-----|*sin(pi + a)
   \  5  /                  \2 + a/
−sin⁡(a+π)cos⁡(πa+2)+tan⁡(16π5)tan⁡(a+π)- \sin{\left(a + \pi \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \tan{\left(\frac{16 \pi}{5} \right)} \tan{\left(a + \pi \right)} 
tan((16*pi)/5)*tan(pi + a) - cos(pi/(2 + a))*sin(pi + a)
Simplificación general [src] 
   _____________                           
  /         ___              /  pi \       
\/  5 - 2*\/ 5  *tan(a) + cos|-----|*sin(a)
                             \2 + a/
sin⁡(a)cos⁡(πa+2)+5−25tan⁡(a)\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)} 
sqrt(5 - 2*sqrt(5))*tan(a) + cos(pi/(2 + a))*sin(a)
Denominador racional [src] 
   _____________                           
  /         ___              /  pi \       
\/  5 - 2*\/ 5  *tan(a) + cos|-----|*sin(a)
                             \2 + a/
sin⁡(a)cos⁡(πa+2)+5−25tan⁡(a)\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)} 
sqrt(5 - 2*sqrt(5))*tan(a) + cos(pi/(2 + a))*sin(a)
Respuesta numérica [src] 
0.726542528005361*tan(pi + a) - cos(pi/(2 + a))*sin(pi + a)
0.726542528005361*tan(pi + a) - cos(pi/(2 + a))*sin(pi + a)
Denominador común [src] 
   _____________                                     
  /         ___                   /  pi \            
\/  5 - 2*\/ 5  *tan(pi + a) - cos|-----|*sin(pi + a)
                                  \2 + a/
−sin⁡(a+π)cos⁡(πa+2)+5−25tan⁡(a+π)- \sin{\left(a + \pi \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a + \pi \right)} 
sqrt(5 - 2*sqrt(5))*tan(pi + a) - cos(pi/(2 + a))*sin(pi + a)
Unión de expresiones racionales [src] 
   _____________                           
  /         ___              /  pi \       
\/  5 - 2*\/ 5  *tan(a) + cos|-----|*sin(a)
                             \2 + a/
sin⁡(a)cos⁡(πa+2)+5−25tan⁡(a)\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)} 
sqrt(5 - 2*sqrt(5))*tan(a) + cos(pi/(2 + a))*sin(a)
Abrimos la expresión [src] 
   _____________                           
  /         ___              /  pi \       
\/  5 - 2*\/ 5  *tan(a) + cos|-----|*sin(a)
                             \2 + a/
sin⁡(a)cos⁡(πa+2)+5−25tan⁡(a)\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)} 
sqrt(5 - 2*sqrt(5))*tan(a) + cos(pi/(2 + a))*sin(a)
Combinatoria [src] 
   _____________                           
  /         ___              /  pi \       
\/  5 - 2*\/ 5  *tan(a) + cos|-----|*sin(a)
                             \2 + a/
sin⁡(a)cos⁡(πa+2)+5−25tan⁡(a)\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)} 
sqrt(5 - 2*sqrt(5))*tan(a) + cos(pi/(2 + a))*sin(a)
Potencias [src] 
  /  pi*I    -pi*I \                                                                                       
  | -----    ------|                                                                                       
  | 2 + a    2 + a |                                                                 /   -4*pi*I    4*pi*I\
  |e        e      | /   I*(-pi - a)    I*(pi + a)\                                  |   -------    ------|
I*|------ + -------|*\- e            + e          /   /   I*(pi + a)    I*(-pi - a)\ |      5         5   |
  \  2         2   /                                  \- e           + e           /*\- e        + e      /
--------------------------------------------------- - -----------------------------------------------------
                         2                                                           / -4*pi*I    4*pi*I\  
                                                                                     | -------    ------|  
                                                        / I*(pi + a)    I*(-pi - a)\ |    5         5   |  
                                                        \e           + e           /*\e        + e      /
i(−ei(−a−π)+ei(a+π))(eiπa+22+e−iπa+22)2−(e4iπ5−e−4iπ5)(ei(−a−π)−ei(a+π))(e−4iπ5+e4iπ5)(ei(−a−π)+ei(a+π))\frac{i \left(- e^{i \left(- a - \pi\right)} + e^{i \left(a + \pi\right)}\right) \left(\frac{e^{\frac{i \pi}{a + 2}}}{2} + \frac{e^{- \frac{i \pi}{a + 2}}}{2}\right)}{2} - \frac{\left(e^{\frac{4 i \pi}{5}} - e^{- \frac{4 i \pi}{5}}\right) \left(e^{i \left(- a - \pi\right)} - e^{i \left(a + \pi\right)}\right)}{\left(e^{- \frac{4 i \pi}{5}} + e^{\frac{4 i \pi}{5}}\right) \left(e^{i \left(- a - \pi\right)} + e^{i \left(a + \pi\right)}\right)} 
   _____________                           
  /         ___              /  pi \       
\/  5 - 2*\/ 5  *tan(a) + cos|-----|*sin(a)
                             \2 + a/
sin⁡(a)cos⁡(πa+2)+5−25tan⁡(a)\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)} 
sqrt(5 - 2*sqrt(5))*tan(a) + cos(pi/(2 + a))*sin(a)
Parte trigonométrica [src] 
                               /       2/    pi   \\    /a\  
   _____________             2*|1 - tan |---------||*cot|-|  
  /         ___                \        \2*(2 + a)//    \2/  
\/  5 - 2*\/ 5  *tan(a) + -----------------------------------
                          /       2/a\\ /       2/    pi   \\
                          |1 + cot |-||*|1 + tan |---------||
                          \        \2// \        \2*(2 + a)//
2(1−tan⁡2(π2(a+2)))cot⁡(a2)(tan⁡2(π2(a+2))+1)(cot⁡2(a2)+1)+5−25tan⁡(a)\frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right) \cot{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)} 
                                  ___    2        
          /pi     pi \        2*\/ 5 *sin (a)     
sin(a)*sin|-- + -----| + -------------------------
          \2    2 + a/      _____________         
                           /         ___          
                         \/  5 + 2*\/ 5  *sin(2*a)
25sin⁡2(a)25+5sin⁡(2a)+sin⁡(a)sin⁡(π2+πa+2)\frac{2 \sqrt{5} \sin^{2}{\left(a \right)}}{\sqrt{2 \sqrt{5} + 5} \sin{\left(2 a \right)}} + \sin{\left(a \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)} 
                         /      ___\            
                         |5   \/ 5 |    /pi    \
                         |- - -----|*csc|-- - a|
          1              \4     4  /    \2     /
---------------------- + -----------------------
          /pi     pi \        ___________       
csc(a)*csc|-- - -----|       /       ___        
          \2    2 + a/      /  5   \/ 5         
                           /   - + ----- *csc(a)
                         \/    8     8
(54−54)csc⁡(−a+π2)58+58csc⁡(a)+1csc⁡(a)csc⁡(π2−πa+2)\frac{\left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \csc{\left(- a + \frac{\pi}{2} \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \csc{\left(a \right)}} + \frac{1}{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 2} \right)}} 
                                /        2/    pi   \\    /a\  
                              2*|-1 + cot |---------||*tan|-|  
            1                   \         \2*(2 + a)//    \2/  
------------------------- + -----------------------------------
     _____________          /       2/    pi   \\ /       2/a\\
    /         ___           |1 + cot |---------||*|1 + tan |-||
   /      2*\/ 5            \        \2*(2 + a)// \        \2//
  /   1 + ------- *cot(a)                                      
\/           5
1255+1cot⁡(a)+2(cot⁡2(π2(a+2))−1)tan⁡(a2)(tan⁡2(a2)+1)(cot⁡2(π2(a+2))+1)\frac{1}{\sqrt{\frac{2 \sqrt{5}}{5} + 1} \cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \tan{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right)} 
       ___________                                             
      /       ___                                              
     /  5   \/ 5                 /       2/    pi   \\    /a\  
    /   - - ----- *tan(a)      2*|1 - tan |---------||*tan|-|  
  \/    8     8                  \        \2*(2 + a)//    \2/  
- ----------------------- + -----------------------------------
                ___         /       2/a\\ /       2/    pi   \\
          1   \/ 5          |1 + tan |-||*|1 + tan |---------||
        - - - -----         \        \2// \        \2*(2 + a)//
          4     4
2(1−tan⁡2(π2(a+2)))tan⁡(a2)(tan⁡2(a2)+1)(tan⁡2(π2(a+2))+1)−58−58tan⁡(a)−54−14\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)} - \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \tan{\left(a \right)}}{- \frac{\sqrt{5}}{4} - \frac{1}{4}} 
                            _____________            
                           /         ___     /pi    \
                         \/  5 - 2*\/ 5  *csc|-- - a|
          1                                  \2     /
---------------------- + ----------------------------
          /pi     pi \              csc(a)           
csc(a)*csc|-- - -----|                               
          \2    2 + a/
5−25csc⁡(−a+π2)csc⁡(a)+1csc⁡(a)csc⁡(π2−πa+2)\frac{\sqrt{5 - 2 \sqrt{5}} \csc{\left(- a + \frac{\pi}{2} \right)}}{\csc{\left(a \right)}} + \frac{1}{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 2} \right)}} 
                         ___________       
                        /       ___        
                       /  5   \/ 5         
                      /   - - ----- *sec(a)
        1           \/    8     8          
----------------- - -----------------------
          /  pi \     /        ___\        
csc(a)*sec|-----|     |  1   \/ 5 |        
          \2 + a/     |- - - -----|*csc(a) 
                      \  4     4  /
−58−58sec⁡(a)(−54−14)csc⁡(a)+1csc⁡(a)sec⁡(πa+2)- \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sec{\left(a \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \csc{\left(a \right)}} + \frac{1}{\csc{\left(a \right)} \sec{\left(\frac{\pi}{a + 2} \right)}} 
                                  ___________            
                           ___   /       ___     /pi    \
                         \/ 2 *\/  5 - \/ 5  *csc|-- - a|
          1                                      \2     /
---------------------- - --------------------------------
          /pi     pi \          /        ___\            
csc(a)*csc|-- - -----|          |  1   \/ 5 |            
          \2    2 + a/        4*|- - - -----|*csc(a)     
                                \  4     4  /
−25−5csc⁡(−a+π2)4(−54−14)csc⁡(a)+1csc⁡(a)csc⁡(π2−πa+2)- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \csc{\left(- a + \frac{\pi}{2} \right)}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \csc{\left(a \right)}} + \frac{1}{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 2} \right)}} 
                              ___    /    pi\   
                            \/ 5 *cos|a - --|   
   /  pi \    /    pi\               \    2 /   
cos|-----|*cos|a - --| + -----------------------
   \2 + a/    \    2 /      _____________       
                           /         ___        
                         \/  5 + 2*\/ 5  *cos(a)
cos⁡(πa+2)cos⁡(a−π2)+5cos⁡(a−π2)25+5cos⁡(a)\cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)} + \frac{\sqrt{5} \cos{\left(a - \frac{\pi}{2} \right)}}{\sqrt{2 \sqrt{5} + 5} \cos{\left(a \right)}} 
    /        2/    pi   \\    /a\               ___________ 
  2*|-1 + cot |---------||*cot|-|        ___   /       ___  
    \         \2*(2 + a)//    \2/      \/ 2 *\/  5 - \/ 5   
----------------------------------- - ----------------------
/       2/a\\ /       2/    pi   \\     /        ___\       
|1 + cot |-||*|1 + cot |---------||     |  1   \/ 5 |       
\        \2// \        \2*(2 + a)//   4*|- - - -----|*cot(a)
                                        \  4     4  /
−25−54(−54−14)cot⁡(a)+2(cot⁡2(π2(a+2))−1)cot⁡(a2)(cot⁡2(a2)+1)(cot⁡2(π2(a+2))+1)- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \cot{\left(\frac{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)} 
                                ___________        
                               /       ___         
                              /  5   \/ 5      2   
                         2*  /   - - ----- *sin (a)
          /pi     pi \     \/    8     8           
sin(a)*sin|-- + -----| - --------------------------
          \2    2 + a/     /        ___\           
                           |  1   \/ 5 |           
                           |- - - -----|*sin(2*a)  
                           \  4     4  /
−258−58sin⁡2(a)(−54−14)sin⁡(2a)+sin⁡(a)sin⁡(π2+πa+2)- \frac{2 \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sin^{2}{\left(a \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \sin{\left(2 a \right)}} + \sin{\left(a \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)} 
     /       2/    pi   \\    /a\              ___________       
   2*|1 - tan |---------||*tan|-|       ___   /       ___        
     \        \2*(2 + a)//    \2/     \/ 2 *\/  5 - \/ 5  *tan(a)
----------------------------------- - ---------------------------
/       2/a\\ /       2/    pi   \\           /        ___\      
|1 + tan |-||*|1 + tan |---------||           |  1   \/ 5 |      
\        \2// \        \2*(2 + a)//         4*|- - - -----|      
                                              \  4     4  /
2(1−tan⁡2(π2(a+2)))tan⁡(a2)(tan⁡2(a2)+1)(tan⁡2(π2(a+2))+1)−25−5tan⁡(a)4(−54−14)\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)} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \tan{\left(a \right)}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right)} 
   _____________                           
  /         ___              /  pi \       
\/  5 - 2*\/ 5  *tan(a) + cos|-----|*sin(a)
                             \2 + a/
sin⁡(a)cos⁡(πa+2)+5−25tan⁡(a)\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)} 
                                   ___               
          1                      \/ 5 *sec(a)        
---------------------- + ----------------------------
   /  pi \    /    pi\      _____________            
sec|-----|*sec|a - --|     /         ___     /    pi\
   \2 + a/    \    2 /   \/  5 + 2*\/ 5  *sec|a - --|
                                             \    2 /
5sec⁡(a)25+5sec⁡(a−π2)+1sec⁡(πa+2)sec⁡(a−π2)\frac{\sqrt{5} \sec{\left(a \right)}}{\sqrt{2 \sqrt{5} + 5} \sec{\left(a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}} 
             ___                                             
       5   \/ 5               /        2/    pi   \\    /a\  
       - - -----            2*|-1 + cot |---------||*cot|-|  
       4     4                \         \2*(2 + a)//    \2/  
----------------------- + -----------------------------------
     ___________          /       2/a\\ /       2/    pi   \\
    /       ___           |1 + cot |-||*|1 + cot |---------||
   /  5   \/ 5            \        \2// \        \2*(2 + a)//
  /   - + ----- *cot(a)                                      
\/    8     8
54−5458+58cot⁡(a)+2(cot⁡2(π2(a+2))−1)cot⁡(a2)(cot⁡2(a2)+1)(cot⁡2(π2(a+2))+1)\frac{\frac{5}{4} - \frac{\sqrt{5}}{4}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \cot{\left(\frac{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)} 
                                  ___________        
                           ___   /       ___     2   
          /pi     pi \   \/ 2 *\/  5 - \/ 5  *sin (a)
sin(a)*sin|-- + -----| - ----------------------------
          \2    2 + a/       /        ___\           
                             |  1   \/ 5 |           
                           2*|- - - -----|*sin(2*a)  
                             \  4     4  /
−25−5sin⁡2(a)2(−54−14)sin⁡(2a)+sin⁡(a)sin⁡(π2+πa+2)- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \sin^{2}{\left(a \right)}}{2 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \sin{\left(2 a \right)}} + \sin{\left(a \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)} 
                                     /      ___\  
                                2    |5   \/ 5 |  
                           2*sin (a)*|- - -----|  
          /pi     pi \               \4     4  /  
sin(a)*sin|-- + -----| + -------------------------
          \2    2 + a/        ___________         
                             /       ___          
                            /  5   \/ 5           
                           /   - + ----- *sin(2*a)
                         \/    8     8
2(54−54)sin⁡2(a)58+58sin⁡(2a)+sin⁡(a)sin⁡(π2+πa+2)\frac{2 \left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \sin^{2}{\left(a \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \sin{\left(2 a \right)}} + \sin{\left(a \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)} 
/      ___\                                             
|5   \/ 5 |               /       2/    pi   \\    /a\  
|- - -----|*tan(a)      2*|1 - tan |---------||*tan|-|  
\4     4  /               \        \2*(2 + a)//    \2/  
------------------ + -----------------------------------
      ___________    /       2/a\\ /       2/    pi   \\
     /       ___     |1 + tan |-||*|1 + tan |---------||
    /  5   \/ 5      \        \2// \        \2*(2 + a)//
   /   - + -----                                        
 \/    8     8
2(1−tan⁡2(π2(a+2)))tan⁡(a2)(tan⁡2(a2)+1)(tan⁡2(π2(a+2))+1)+(54−54)tan⁡(a)58+58\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)} + \frac{\left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \tan{\left(a \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}} 
                         ___________       
                        /       ___        
                       /  5   \/ 5         
                      /   - - ----- *tan(a)
   /  pi \          \/    8     8          
cos|-----|*sin(a) - -----------------------
   \2 + a/                        ___      
                            1   \/ 5       
                          - - - -----      
                            4     4
sin⁡(a)cos⁡(πa+2)−58−58tan⁡(a)−54−14\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} - \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \tan{\left(a \right)}}{- \frac{\sqrt{5}}{4} - \frac{1}{4}} 
                                 ___________        
                                /       ___         
                               /  5   \/ 5          
                              /   - - ----- *sec(a) 
            1               \/    8     8           
- ---------------------- - -------------------------
     /  pi \    /    pi\   /        ___\            
  sec|-----|*sec|a + --|   |  1   \/ 5 |    /    pi\
     \2 + a/    \    2 /   |- - - -----|*sec|a - --|
                           \  4     4  /    \    2 /
−58−58sec⁡(a)(−54−14)sec⁡(a−π2)−1sec⁡(πa+2)sec⁡(a+π2)- \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sec{\left(a \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \sec{\left(a - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(a + \frac{\pi}{2} \right)}} 
                        ___         
   /  pi \            \/ 5 *tan(a)  
cos|-----|*sin(a) + ----------------
   \2 + a/             _____________
                      /         ___ 
                    \/  5 + 2*\/ 5
sin⁡(a)cos⁡(πa+2)+5tan⁡(a)25+5\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \frac{\sqrt{5} \tan{\left(a \right)}}{\sqrt{2 \sqrt{5} + 5}} 
                              /        2/    pi   \\    /a\  
           ___              2*|-1 + cot |---------||*cot|-|  
         \/ 5                 \         \2*(2 + a)//    \2/  
----------------------- + -----------------------------------
   _____________          /       2/a\\ /       2/    pi   \\
  /         ___           |1 + cot |-||*|1 + cot |---------||
\/  5 + 2*\/ 5  *cot(a)   \        \2// \        \2*(2 + a)//
525+5cot⁡(a)+2(cot⁡2(π2(a+2))−1)cot⁡(a2)(cot⁡2(a2)+1)(cot⁡2(π2(a+2))+1)\frac{\sqrt{5}}{\sqrt{2 \sqrt{5} + 5} \cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \cot{\left(\frac{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)} 
                              ___    /pi    \   
                            \/ 5 *csc|-- - a|   
          1                          \2     /   
---------------------- + -----------------------
          /pi     pi \      _____________       
csc(a)*csc|-- - -----|     /         ___        
          \2    2 + a/   \/  5 + 2*\/ 5  *csc(a)
5csc⁡(−a+π2)25+5csc⁡(a)+1csc⁡(a)csc⁡(π2−πa+2)\frac{\sqrt{5} \csc{\left(- a + \frac{\pi}{2} \right)}}{\sqrt{2 \sqrt{5} + 5} \csc{\left(a \right)}} + \frac{1}{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 2} \right)}} 
                              ___________            
                             /       ___             
                            /  5   \/ 5      /    pi\
                           /   - - ----- *cos|a - --|
   /  pi \    /    pi\   \/    8     8       \    2 /
cos|-----|*cos|a - --| - ----------------------------
   \2 + a/    \    2 /       /        ___\           
                             |  1   \/ 5 |           
                             |- - - -----|*cos(a)    
                             \  4     4  /
cos⁡(πa+2)cos⁡(a−π2)−58−58cos⁡(a−π2)(−54−14)cos⁡(a)\cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)} - \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \cos{\left(a - \frac{\pi}{2} \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \cos{\left(a \right)}} 
   /      pi \      /      pi \            ___________       
sin|a + -----| + sin|a - -----|     ___   /       ___        
   \    2 + a/      \    2 + a/   \/ 2 *\/  5 - \/ 5  *tan(a)
------------------------------- - ---------------------------
               2                          /        ___\      
                                          |  1   \/ 5 |      
                                        4*|- - - -----|      
                                          \  4     4  /
sin⁡(a−πa+2)+sin⁡(a+πa+2)2−25−5tan⁡(a)4(−54−14)\frac{\sin{\left(a - \frac{\pi}{a + 2} \right)} + \sin{\left(a + \frac{\pi}{a + 2} \right)}}{2} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \tan{\left(a \right)}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right)} 
                              /      ___\            
                              |5   \/ 5 |            
                              |- - -----|*sec(a)     
          1                   \4     4  /            
---------------------- + ----------------------------
   /  pi \    /    pi\        ___________            
sec|-----|*sec|a - --|       /       ___             
   \2 + a/    \    2 /      /  5   \/ 5      /    pi\
                           /   - + ----- *sec|a - --|
                         \/    8     8       \    2 /
(54−54)sec⁡(a)58+58sec⁡(a−π2)+1sec⁡(πa+2)sec⁡(a−π2)\frac{\left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \sec{\left(a \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \sec{\left(a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}} 
                         ___________       
                        /       ___        
                       /  5   \/ 5         
                      /   - - ----- *sin(a)
   /  pi \          \/    8     8          
cos|-----|*sin(a) - -----------------------
   \2 + a/            /        ___\        
                      |  1   \/ 5 |        
                      |- - - -----|*cos(a) 
                      \  4     4  /
sin⁡(a)cos⁡(πa+2)−58−58sin⁡(a)(−54−14)cos⁡(a)\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} - \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sin{\left(a \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \cos{\left(a \right)}} 
                                     /       2/    pi   \\          
   _____________                   2*|1 - tan |---------||          
  /         ___                      \        \2*(2 + a)//          
\/  5 - 2*\/ 5  *tan(a) + ------------------------------------------
                          /       1   \ /       2/    pi   \\    /a\
                          |1 + -------|*|1 + tan |---------||*tan|-|
                          |       2/a\| \        \2*(2 + a)//    \2/
                          |    tan |-||                             
                          \        \2//
5−25tan⁡(a)+2(1−tan⁡2(π2(a+2)))(1+1tan⁡2(a2))(tan⁡2(π2(a+2))+1)tan⁡(a2)\sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)} + \frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right)}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \tan{\left(\frac{a}{2} \right)}} 
   _____________       /        2/    pi   \\    /a\  
  /         ___      2*|-1 + cot |---------||*cot|-|  
\/  5 - 2*\/ 5         \         \2*(2 + a)//    \2/  
---------------- + -----------------------------------
     cot(a)        /       2/a\\ /       2/    pi   \\
                   |1 + cot |-||*|1 + cot |---------||
                   \        \2// \        \2*(2 + a)//
5−25cot⁡(a)+2(cot⁡2(π2(a+2))−1)cot⁡(a2)(cot⁡2(a2)+1)(cot⁡2(π2(a+2))+1)\frac{\sqrt{5 - 2 \sqrt{5}}}{\cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \cot{\left(\frac{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)} 
                                  /      ___\       
   /      pi \      /      pi \   |5   \/ 5 |       
sin|a + -----| + sin|a - -----|   |- - -----|*tan(a)
   \    2 + a/      \    2 + a/   \4     4  /       
------------------------------- + ------------------
               2                        ___________ 
                                       /       ___  
                                      /  5   \/ 5   
                                     /   - + -----  
                                   \/    8     8
sin⁡(a−πa+2)+sin⁡(a+πa+2)2+(54−54)tan⁡(a)58+58\frac{\sin{\left(a - \frac{\pi}{a + 2} \right)} + \sin{\left(a + \frac{\pi}{a + 2} \right)}}{2} + \frac{\left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \tan{\left(a \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}} 
                        /       2/    pi   \\    /a\  
    ___               2*|1 - tan |---------||*tan|-|  
  \/ 5 *tan(a)          \        \2*(2 + a)//    \2/  
---------------- + -----------------------------------
   _____________   /       2/a\\ /       2/    pi   \\
  /         ___    |1 + tan |-||*|1 + tan |---------||
\/  5 + 2*\/ 5     \        \2// \        \2*(2 + a)//
2(1−tan⁡2(π2(a+2)))tan⁡(a2)(tan⁡2(a2)+1)(tan⁡2(π2(a+2))+1)+5tan⁡(a)25+5\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)} + \frac{\sqrt{5} \tan{\left(a \right)}}{\sqrt{2 \sqrt{5} + 5}} 
                                  ___________       
                           ___   /       ___        
          1              \/ 2 *\/  5 - \/ 5  *sec(a)
---------------------- - ---------------------------
   /  pi \    /    pi\     /        ___\            
sec|-----|*sec|a - --|     |  1   \/ 5 |    /    pi\
   \2 + a/    \    2 /   4*|- - - -----|*sec|a - --|
                           \  4     4  /    \    2 /
−25−5sec⁡(a)4(−54−14)sec⁡(a−π2)+1sec⁡(πa+2)sec⁡(a−π2)- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \sec{\left(a \right)}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \sec{\left(a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}} 
                                /      ___\  
                           2    |5   \/ 5 |  
                      2*sin (a)*|- - -----|  
   /  pi \                      \4     4  /  
cos|-----|*sin(a) + -------------------------
   \2 + a/               ___________         
                        /       ___          
                       /  5   \/ 5           
                      /   - + ----- *sin(2*a)
                    \/    8     8
2(54−54)sin⁡2(a)58+58sin⁡(2a)+sin⁡(a)cos⁡(πa+2)\frac{2 \left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \sin^{2}{\left(a \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \sin{\left(2 a \right)}} + \sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} 
         ___________                                        
        /       ___                                         
       /  5   \/ 5           /        2/    pi   \\    /a\  
      /   - - -----        2*|-1 + cot |---------||*cot|-|  
    \/    8     8            \         \2*(2 + a)//    \2/  
- -------------------- + -----------------------------------
  /        ___\          /       2/a\\ /       2/    pi   \\
  |  1   \/ 5 |          |1 + cot |-||*|1 + cot |---------||
  |- - - -----|*cot(a)   \        \2// \        \2*(2 + a)//
  \  4     4  /
−58−58(−54−14)cot⁡(a)+2(cot⁡2(π2(a+2))−1)cot⁡(a2)(cot⁡2(a2)+1)(cot⁡2(π2(a+2))+1)- \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \cot{\left(\frac{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)} 
                             ___________       
                      ___   /       ___        
   /  pi \          \/ 2 *\/  5 - \/ 5  *tan(a)
cos|-----|*sin(a) - ---------------------------
   \2 + a/                  /        ___\      
                            |  1   \/ 5 |      
                          4*|- - - -----|      
                            \  4     4  /
sin⁡(a)cos⁡(πa+2)−25−5tan⁡(a)4(−54−14)\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \tan{\left(a \right)}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right)} 
                              _____________        
                             /         ___     2   
          /pi     pi \   2*\/  5 - 2*\/ 5  *sin (a)
sin(a)*sin|-- + -----| + --------------------------
          \2    2 + a/            sin(2*a)
25−25sin⁡2(a)sin⁡(2a)+sin⁡(a)sin⁡(π2+πa+2)\frac{2 \sqrt{5 - 2 \sqrt{5}} \sin^{2}{\left(a \right)}}{\sin{\left(2 a \right)}} + \sin{\left(a \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)} 
                              ___________            
                             /       ___             
                            /  5   \/ 5      /pi    \
                           /   - - ----- *csc|-- - a|
          1              \/    8     8       \2     /
---------------------- - ----------------------------
          /pi     pi \       /        ___\           
csc(a)*csc|-- - -----|       |  1   \/ 5 |           
          \2    2 + a/       |- - - -----|*csc(a)    
                             \  4     4  /
−58−58csc⁡(−a+π2)(−54−14)csc⁡(a)+1csc⁡(a)csc⁡(π2−πa+2)- \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \csc{\left(- a + \frac{\pi}{2} \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \csc{\left(a \right)}} + \frac{1}{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 2} \right)}} 
                                       ___________       
                                      /       ___        
   /      pi \      /      pi \      /  5   \/ 5         
sin|a + -----| + sin|a - -----|     /   - - ----- *tan(a)
   \    2 + a/      \    2 + a/   \/    8     8          
------------------------------- - -----------------------
               2                                ___      
                                          1   \/ 5       
                                        - - - -----      
                                          4     4
sin⁡(a−πa+2)+sin⁡(a+πa+2)2−58−58tan⁡(a)−54−14\frac{\sin{\left(a - \frac{\pi}{a + 2} \right)} + \sin{\left(a + \frac{\pi}{a + 2} \right)}}{2} - \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \tan{\left(a \right)}}{- \frac{\sqrt{5}}{4} - \frac{1}{4}} 
                                  ___________            
                           ___   /       ___     /    pi\
                         \/ 2 *\/  5 - \/ 5  *cos|a - --|
   /  pi \    /    pi\                           \    2 /
cos|-----|*cos|a - --| - --------------------------------
   \2 + a/    \    2 /          /        ___\            
                                |  1   \/ 5 |            
                              4*|- - - -----|*cos(a)     
                                \  4     4  /
cos⁡(πa+2)cos⁡(a−π2)−25−5cos⁡(a−π2)4(−54−14)cos⁡(a)\cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \cos{\left(a - \frac{\pi}{2} \right)}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \cos{\left(a \right)}} 
                              /27*pi\    /    pi\
                           cos|-----|*cos|a + --|
     /  pi \    /    pi\      \  10 /    \    2 /
- cos|-----|*cos|a + --| - ----------------------
     \2 + a/    \    2 /    /        ___\        
                            |  1   \/ 5 |        
                            |- - - -----|*cos(a) 
                            \  4     4  /
−cos⁡(πa+2)cos⁡(a+π2)−cos⁡(27π10)cos⁡(a+π2)(−54−14)cos⁡(a)- \cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(a + \frac{\pi}{2} \right)} - \frac{\cos{\left(\frac{27 \pi}{10} \right)} \cos{\left(a + \frac{\pi}{2} \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \cos{\left(a \right)}} 
                               /       2/    pi   \\    /a\  
   _____________             2*|1 - tan |---------||*tan|-|  
  /         ___                \        \2*(2 + a)//    \2/  
\/  5 - 2*\/ 5  *tan(a) + -----------------------------------
                          /       2/a\\ /       2/    pi   \\
                          |1 + tan |-||*|1 + tan |---------||
                          \        \2// \        \2*(2 + a)//
2(1−tan⁡2(π2(a+2)))tan⁡(a2)(tan⁡2(a2)+1)(tan⁡2(π2(a+2))+1)+5−25tan⁡(a)\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)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)} 
                                       /        2/    pi   \\         
                                     2*|-1 + cot |---------||         
            1                          \         \2*(2 + a)//         
------------------------- + ------------------------------------------
     _____________          /       1   \ /       2/    pi   \\    /a\
    /         ___           |1 + -------|*|1 + cot |---------||*cot|-|
   /      2*\/ 5            |       2/a\| \        \2*(2 + a)//    \2/
  /   1 + ------- *cot(a)   |    cot |-||                             
\/           5              \        \2//
1255+1cot⁡(a)+2(cot⁡2(π2(a+2))−1)(1+1cot⁡2(a2))(cot⁡2(π2(a+2))+1)cot⁡(a2)\frac{1}{\sqrt{\frac{2 \sqrt{5}}{5} + 1} \cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right)}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \cot{\left(\frac{a}{2} \right)}} 
                            _____________       
                           /         ___        
          1              \/  5 - 2*\/ 5  *sec(a)
---------------------- + -----------------------
   /  pi \    /    pi\            /    pi\      
sec|-----|*sec|a - --|         sec|a - --|      
   \2 + a/    \    2 /            \    2 /
5−25sec⁡(a)sec⁡(a−π2)+1sec⁡(πa+2)sec⁡(a−π2)\frac{\sqrt{5 - 2 \sqrt{5}} \sec{\left(a \right)}}{\sec{\left(a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}} 
                            _____________            
                           /         ___     /    pi\
                         \/  5 - 2*\/ 5  *cos|a - --|
   /  pi \    /    pi\                       \    2 /
cos|-----|*cos|a - --| + ----------------------------
   \2 + a/    \    2 /              cos(a)
cos⁡(πa+2)cos⁡(a−π2)+5−25cos⁡(a−π2)cos⁡(a)\cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)} + \frac{\sqrt{5 - 2 \sqrt{5}} \cos{\left(a - \frac{\pi}{2} \right)}}{\cos{\left(a \right)}} 
                         /      ___\            
                         |5   \/ 5 |    /    pi\
                         |- - -----|*cos|a - --|
   /  pi \    /    pi\   \4     4  /    \    2 /
cos|-----|*cos|a - --| + -----------------------
   \2 + a/    \    2 /        ___________       
                             /       ___        
                            /  5   \/ 5         
                           /   - + ----- *cos(a)
                         \/    8     8
cos⁡(πa+2)cos⁡(a−π2)+(54−54)cos⁡(a−π2)58+58cos⁡(a)\cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)} + \frac{\left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \cos{\left(a - \frac{\pi}{2} \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \cos{\left(a \right)}} 
                    /      ___\       
                    |5   \/ 5 |       
                    |- - -----|*tan(a)
   /  pi \          \4     4  /       
cos|-----|*sin(a) + ------------------
   \2 + a/                ___________ 
                         /       ___  
                        /  5   \/ 5   
                       /   - + -----  
                     \/    8     8
sin⁡(a)cos⁡(πa+2)+(54−54)tan⁡(a)58+58\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \frac{\left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \tan{\left(a \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}} 
                               ___________        
                              /       ___         
                             /  5   \/ 5          
                            /   - - ----- *sec(a) 
          1               \/    8     8           
---------------------- - -------------------------
   /  pi \    /    pi\   /        ___\            
sec|-----|*sec|a - --|   |  1   \/ 5 |    /    pi\
   \2 + a/    \    2 /   |- - - -----|*sec|a - --|
                         \  4     4  /    \    2 /
−58−58sec⁡(a)(−54−14)sec⁡(a−π2)+1sec⁡(πa+2)sec⁡(a−π2)- \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sec{\left(a \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \sec{\left(a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}} 
1/(sec(pi/(2 + a))*sec(a - pi/2)) - sqrt(5/8 - sqrt(5)/8)*sec(a)/((-1/4 - sqrt(5)/4)*sec(a - pi/2))
    © Sr Examen – Калькулятор