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y^4-9*y^2-2
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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(2*a)-2*sin(a/(2-15))*cos(a/2+15)

¿Cómo vas a descomponer esta sin(2a)-2sin(a/(2-15))*cos(a/2+15) expresión en fracciones?

Solución

Ha introducido [src]

                / a \    /a     \
sin(2*a) - 2*sin|---|*cos|- + 15|
                \-13/    \2     /

\sin{\left(2 a \right)} - 2 \sin{\left(\frac{a}{-13} \right)} \cos{\left(\frac{a}{2} + 15 \right)}

sin(2*a) - 2*sin(a/(-13))*cos(a/2 + 15)

Simplificación general [src]

     /     a\    /a \           
2*cos|15 + -|*sin|--| + sin(2*a)
     \     2/    \13/

2 \sin{\left(\frac{a}{13} \right)} \cos{\left(\frac{a}{2} + 15 \right)} + \sin{\left(2 a \right)}

2*cos(15 + a/2)*sin(a/13) + sin(2*a)

Respuesta numérica [src]

-2.0*cos(a/2 + 15)*sin(a/(-13)) + sin(2*a)

-2.0*cos(a/2 + 15)*sin(a/(-13)) + sin(2*a)

Denominador común [src]

     /     a\    /a \           
2*cos|15 + -|*sin|--| + sin(2*a)
     \     2/    \13/

2 \sin{\left(\frac{a}{13} \right)} \cos{\left(\frac{a}{2} + 15 \right)} + \sin{\left(2 a \right)}

2*cos(15 + a/2)*sin(a/13) + sin(2*a)

Unión de expresiones racionales [src]

     /30 + a\    /a \           
2*cos|------|*sin|--| + sin(2*a)
     \  2   /    \13/

2 \sin{\left(\frac{a}{13} \right)} \cos{\left(\frac{a + 30}{2} \right)} + \sin{\left(2 a \right)}

2*cos((30 + a)/2)*sin(a/13) + sin(2*a)

Potencias [src]

     /     a\    /a \           
2*cos|15 + -|*sin|--| + sin(2*a)
     \     2/    \13/

2 \sin{\left(\frac{a}{13} \right)} \cos{\left(\frac{a}{2} + 15 \right)} + \sin{\left(2 a \right)}

                             /   /      a\      /     a\\                  
                             | I*|-15 - -|    I*|15 + -|| /   I*a    -I*a \
    /   -2*I*a    2*I*a\     |   \      2/      \     2/| |   ---    -----|
  I*\- e       + e     /     |e              e          | |    13      13 |
- ---------------------- + I*|------------ + -----------|*\- e    + e     /
            2                \     2              2     /

i \left(- e^{\frac{i a}{13}} + e^{- \frac{i a}{13}}\right) \left(\frac{e^{i \left(- \frac{a}{2} - 15\right)}}{2} + \frac{e^{i \left(\frac{a}{2} + 15\right)}}{2}\right) - \frac{i \left(e^{2 i a} - e^{- 2 i a}\right)}{2}

-i*(-exp(-2*i*a) + exp(2*i*a))/2 + i*(exp(i*(-15 - a/2))/2 + exp(i*(15 + a/2))/2)*(-exp(i*a/13) + exp(-i*a/13))

Combinatoria [src]

     /     a\    /a \           
2*cos|15 + -|*sin|--| + sin(2*a)
     \     2/    \13/

2 \sin{\left(\frac{a}{13} \right)} \cos{\left(\frac{a}{2} + 15 \right)} + \sin{\left(2 a \right)}

2*cos(15 + a/2)*sin(a/13) + sin(2*a)

Abrimos la expresión [src]

                            9       /a\    /a \             9       /a\    /a \             13       /a\    /a \             13       /a\    /a \            5       /a\    /a \            5       /a\    /a \                /a\    /a \                /a\    /a \           3       /a\    /a \           3       /a\    /a \            15       /a\    /a \            15       /a\    /a \            7       /a\    /a \            7       /a\    /a \             11       /a\    /a \             11       /a\    /a \
2*cos(a)*sin(a) - 140800*cos (1)*cos|-|*sin|--| - 140800*sin (1)*sin|-|*sin|--| - 122880*cos  (1)*cos|-|*sin|--| - 122880*sin  (1)*sin|-|*sin|--| - 12096*cos (1)*cos|-|*sin|--| - 12096*sin (1)*sin|-|*sin|--| - 30*cos(1)*cos|-|*sin|--| - 30*sin(1)*sin|-|*sin|--| + 1120*cos (1)*cos|-|*sin|--| + 1120*sin (1)*sin|-|*sin|--| + 32768*cos  (1)*cos|-|*sin|--| + 32768*sin  (1)*sin|-|*sin|--| + 57600*cos (1)*cos|-|*sin|--| + 57600*sin (1)*sin|-|*sin|--| + 184320*cos  (1)*cos|-|*sin|--| + 184320*sin  (1)*sin|-|*sin|--|
                                    \2/    \13/                     \2/    \13/                      \2/    \13/                      \2/    \13/                    \2/    \13/                    \2/    \13/                \2/    \13/                \2/    \13/                   \2/    \13/                   \2/    \13/                     \2/    \13/                     \2/    \13/                    \2/    \13/                    \2/    \13/                      \2/    \13/                      \2/    \13/

- 140800 \sin^{9}{\left(1 \right)} \sin{\left(\frac{a}{13} \right)} \sin{\left(\frac{a}{2} \right)} - 122880 \sin^{13}{\left(1 \right)} \sin{\left(\frac{a}{13} \right)} \sin{\left(\frac{a}{2} \right)} - 12096 \sin^{5}{\left(1 \right)} \sin{\left(\frac{a}{13} \right)} \sin{\left(\frac{a}{2} \right)} - 30 \sin{\left(1 \right)} \sin{\left(\frac{a}{13} \right)} \sin{\left(\frac{a}{2} \right)} + 1120 \sin^{3}{\left(1 \right)} \sin{\left(\frac{a}{13} \right)} \sin{\left(\frac{a}{2} \right)} + 32768 \sin^{15}{\left(1 \right)} \sin{\left(\frac{a}{13} \right)} \sin{\left(\frac{a}{2} \right)} + 57600 \sin^{7}{\left(1 \right)} \sin{\left(\frac{a}{13} \right)} \sin{\left(\frac{a}{2} \right)} + 184320 \sin^{11}{\left(1 \right)} \sin{\left(\frac{a}{13} \right)} \sin{\left(\frac{a}{2} \right)} - 12096 \sin{\left(\frac{a}{13} \right)} \cos^{5}{\left(1 \right)} \cos{\left(\frac{a}{2} \right)} - 140800 \sin{\left(\frac{a}{13} \right)} \cos^{9}{\left(1 \right)} \cos{\left(\frac{a}{2} \right)} - 122880 \sin{\left(\frac{a}{13} \right)} \cos^{13}{\left(1 \right)} \cos{\left(\frac{a}{2} \right)} - 30 \sin{\left(\frac{a}{13} \right)} \cos{\left(1 \right)} \cos{\left(\frac{a}{2} \right)} + 32768 \sin{\left(\frac{a}{13} \right)} \cos^{15}{\left(1 \right)} \cos{\left(\frac{a}{2} \right)} + 1120 \sin{\left(\frac{a}{13} \right)} \cos^{3}{\left(1 \right)} \cos{\left(\frac{a}{2} \right)} + 184320 \sin{\left(\frac{a}{13} \right)} \cos^{11}{\left(1 \right)} \cos{\left(\frac{a}{2} \right)} + 57600 \sin{\left(\frac{a}{13} \right)} \cos^{7}{\left(1 \right)} \cos{\left(\frac{a}{2} \right)} + 2 \sin{\left(a \right)} \cos{\left(a \right)}

2*cos(a)*sin(a) - 140800*cos(1)^9*cos(a/2)*sin(a/13) - 140800*sin(1)^9*sin(a/2)*sin(a/13) - 122880*cos(1)^13*cos(a/2)*sin(a/13) - 122880*sin(1)^13*sin(a/2)*sin(a/13) - 12096*cos(1)^5*cos(a/2)*sin(a/13) - 12096*sin(1)^5*sin(a/2)*sin(a/13) - 30*cos(1)*cos(a/2)*sin(a/13) - 30*sin(1)*sin(a/2)*sin(a/13) + 1120*cos(1)^3*cos(a/2)*sin(a/13) + 1120*sin(1)^3*sin(a/2)*sin(a/13) + 32768*cos(1)^15*cos(a/2)*sin(a/13) + 32768*sin(1)^15*sin(a/2)*sin(a/13) + 57600*cos(1)^7*cos(a/2)*sin(a/13) + 57600*sin(1)^7*sin(a/2)*sin(a/13) + 184320*cos(1)^11*cos(a/2)*sin(a/13) + 184320*sin(1)^11*sin(a/2)*sin(a/13)

Parte trigonométrica [src]

                            /          2/15   a\  \           
                            |       sec |-- + -|  |           
                            |           \2    4/  |           
                          4*|1 - -----------------|           
                            |       2/15   pi   a\|           
                            |    sec |-- - -- + -||           
      1                     \        \2    2    4//           
------------- + ----------------------------------------------
   /      pi\   /          2/15   a\  \                       
sec|2*a - --|   |       sec |-- + -|  |                       
   \      2 /   |           \2    4/  |    /a \    /  pi   a \
                |1 + -----------------|*sec|--|*sec|- -- + --|
                |       2/15   pi   a\|    \26/    \  2    26/
                |    sec |-- - -- + -||                       
                \        \2    2    4//

\frac{4 \left(- \frac{\sec^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}{\sec^{2}{\left(\frac{a}{4} - \frac{\pi}{2} + \frac{15}{2} \right)}} + 1\right)}{\left(\frac{\sec^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}{\sec^{2}{\left(\frac{a}{4} - \frac{\pi}{2} + \frac{15}{2} \right)}} + 1\right) \sec{\left(\frac{a}{26} \right)} \sec{\left(\frac{a}{26} - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(2 a - \frac{\pi}{2} \right)}}

         /15   11*a\           /15   15*a\            
    2*tan|-- + ----|      2*tan|-- + ----|            
         \2     52 /           \2     52 /            
- ------------------- + ------------------- + sin(2*a)
         2/15   11*a\          2/15   15*a\           
  1 + tan |-- + ----|   1 + tan |-- + ----|           
          \2     52 /           \2     52 /

\sin{\left(2 a \right)} + \frac{2 \tan{\left(\frac{15 a}{52} + \frac{15}{2} \right)}}{\tan^{2}{\left(\frac{15 a}{52} + \frac{15}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{11 a}{52} + \frac{15}{2} \right)}}{\tan^{2}{\left(\frac{11 a}{52} + \frac{15}{2} \right)} + 1}

     /     pi   11*a\      /      pi\      /     pi   15*a\
- cos|15 - -- + ----| + cos|2*a - --| + cos|15 - -- + ----|
     \     2     26 /      \      2 /      \     2     26 /

\cos{\left(2 a - \frac{\pi}{2} \right)} - \cos{\left(\frac{11 a}{26} - \frac{\pi}{2} + 15 \right)} + \cos{\left(\frac{15 a}{26} - \frac{\pi}{2} + 15 \right)}

   1             1                1       
-------- + -------------- - --------------
csc(2*a)      /     15*a\      /     11*a\
           csc|15 + ----|   csc|15 + ----|
              \      26 /      \      26 /

\frac{1}{\csc{\left(\frac{15 a}{26} + 15 \right)}} - \frac{1}{\csc{\left(\frac{11 a}{26} + 15 \right)}} + \frac{1}{\csc{\left(2 a \right)}}

     /     a\    /  pi   a \      /      pi\
2*cos|15 + -|*cos|- -- + --| + cos|2*a - --|
     \     2/    \  2    13/      \      2 /

2 \cos{\left(\frac{a}{13} - \frac{\pi}{2} \right)} \cos{\left(\frac{a}{2} + 15 \right)} + \cos{\left(2 a - \frac{\pi}{2} \right)}

       /     a\    /  pi   a \      /      pi\
- 2*cos|15 + -|*cos|- -- - --| + cos|2*a - --|
       \     2/    \  2    13/      \      2 /

- 2 \cos{\left(- \frac{a}{13} - \frac{\pi}{2} \right)} \cos{\left(\frac{a}{2} + 15 \right)} + \cos{\left(2 a - \frac{\pi}{2} \right)}

                   /       2/15   a\\    /a \  
                 4*|1 - tan |-- + -||*tan|--|  
  2*tan(a)         \        \2    4//    \26/  
----------- + ---------------------------------
       2      /       2/a \\ /       2/15   a\\
1 + tan (a)   |1 + tan |--||*|1 + tan |-- + -||
              \        \26// \        \2    4//

\frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}\right) \tan{\left(\frac{a}{26} \right)}}{\left(\tan^{2}{\left(\frac{a}{26} \right)} + 1\right) \left(\tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1\right)} + \frac{2 \tan{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1}

   1                2         
-------- + -------------------
csc(2*a)      /a \    /     a\
           csc|--|*sec|15 + -|
              \13/    \     2/

\frac{1}{\csc{\left(2 a \right)}} + \frac{2}{\csc{\left(\frac{a}{13} \right)} \sec{\left(\frac{a}{2} + 15 \right)}}

  /       2/15   a\\    /a \    /a \           
4*|1 - tan |-- + -||*cos|--|*sin|--|           
  \        \2    4//    \26/    \26/           
------------------------------------ + sin(2*a)
                 2/15   a\                     
          1 + tan |-- + -|                     
                  \2    4/

\frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}\right) \sin{\left(\frac{a}{26} \right)} \cos{\left(\frac{a}{26} \right)}}{\tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1} + \sin{\left(2 a \right)}

     /     11*a\                 /     15*a\
- sin|15 + ----| + sin(2*a) + sin|15 + ----|
     \      26 /                 \      26 /

\sin{\left(2 a \right)} - \sin{\left(\frac{11 a}{26} + 15 \right)} + \sin{\left(\frac{15 a}{26} + 15 \right)}

                2                                               
  /       2/a \\     4/a \ /       2/15   a\\    /a \           
4*|1 - tan |--|| *cos |--|*|1 - tan |-- + -||*tan|--|           
  \        \52//      \52/ \        \2    4//    \26/           
----------------------------------------------------- + sin(2*a)
                          2/15   a\                             
                   1 + tan |-- + -|                             
                           \2    4/

\frac{4 \left(1 - \tan^{2}{\left(\frac{a}{52} \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}\right) \cos^{4}{\left(\frac{a}{52} \right)} \tan{\left(\frac{a}{26} \right)}}{\tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1} + \sin{\left(2 a \right)}

      1                     2             
------------- + --------------------------
   /      pi\      /     a\    /  pi   a \
sec|2*a - --|   sec|15 + -|*sec|- -- + --|
   \      2 /      \     2/    \  2    13/

\frac{1}{\sec{\left(2 a - \frac{\pi}{2} \right)}} + \frac{2}{\sec{\left(\frac{a}{13} - \frac{\pi}{2} \right)} \sec{\left(\frac{a}{2} + 15 \right)}}

      1                     2             
------------- - --------------------------
   /      pi\      /     a\    /  pi   a \
sec|2*a - --|   sec|15 + -|*sec|- -- - --|
   \      2 /      \     2/    \  2    13/

\frac{1}{\sec{\left(2 a - \frac{\pi}{2} \right)}} - \frac{2}{\sec{\left(- \frac{a}{13} - \frac{\pi}{2} \right)} \sec{\left(\frac{a}{2} + 15 \right)}}

                                 2                      
                  /        2/a \\  /         1      \   
                4*|-1 + cot |--|| *|1 - ------------|   
                  \         \52//  |       2/15   a\|   
                                   |    cot |-- + -||   
  2*cot(a)                         \        \2    4//   
----------- + ------------------------------------------
       2                    2                           
1 + cot (a)   /       2/a \\  /         1      \    /a \
              |1 + cot |--|| *|1 + ------------|*cot|--|
              \        \52//  |       2/15   a\|    \26/
                              |    cot |-- + -||        
                              \        \2    4//

\frac{4 \left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{a}{52} \right)} - 1\right)^{2}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{a}{52} \right)} + 1\right)^{2} \cot{\left(\frac{a}{26} \right)}} + \frac{2 \cot{\left(a \right)}}{\cot^{2}{\left(a \right)} + 1}

                         /         4/15   a\\           
                         |    4*sin |-- + -||           
     2/a \    2/pi   a \ |          \2    4/|           
8*sin |--|*sin |-- + --|*|1 - --------------|           
      \26/     \2    26/ |        2/     a\ |           
                         |     sin |15 + -| |           
                         \         \     2/ /           
--------------------------------------------- + sin(2*a)
         /         4/15   a\\                           
         |    4*sin |-- + -||                           
         |          \2    4/|    /a \                   
         |1 + --------------|*sin|--|                   
         |        2/     a\ |    \13/                   
         |     sin |15 + -| |                           
         \         \     2/ /

\frac{8 \left(- \frac{4 \sin^{4}{\left(\frac{a}{4} + \frac{15}{2} \right)}}{\sin^{2}{\left(\frac{a}{2} + 15 \right)}} + 1\right) \sin^{2}{\left(\frac{a}{26} \right)} \sin^{2}{\left(\frac{a}{26} + \frac{\pi}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{4} + \frac{15}{2} \right)}}{\sin^{2}{\left(\frac{a}{2} + 15 \right)}} + 1\right) \sin{\left(\frac{a}{13} \right)}} + \sin{\left(2 a \right)}

                              2                           
                /       2/a \\  /       2/15   a\\    /a \
              4*|1 - tan |--|| *|1 - tan |-- + -||*tan|--|
  2*tan(a)      \        \52//  \        \2    4//    \26/
----------- + --------------------------------------------
       2                         2                        
1 + tan (a)        /       2/a \\  /       2/15   a\\     
                   |1 + tan |--|| *|1 + tan |-- + -||     
                   \        \52//  \        \2    4//

\frac{4 \left(1 - \tan^{2}{\left(\frac{a}{52} \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}\right) \tan{\left(\frac{a}{26} \right)}}{\left(\tan^{2}{\left(\frac{a}{52} \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1\right)} + \frac{2 \tan{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1}

         /15   11*a\                         /15   15*a\ 
    2*cot|-- + ----|                    2*cot|-- + ----| 
         \2     52 /      2*cot(a)           \2     52 / 
- ------------------- + ----------- + -------------------
         2/15   11*a\          2             2/15   15*a\
  1 + cot |-- + ----|   1 + cot (a)   1 + cot |-- + ----|
          \2     52 /                         \2     52 /

\frac{2 \cot{\left(\frac{15 a}{52} + \frac{15}{2} \right)}}{\cot^{2}{\left(\frac{15 a}{52} + \frac{15}{2} \right)} + 1} - \frac{2 \cot{\left(\frac{11 a}{52} + \frac{15}{2} \right)}}{\cot^{2}{\left(\frac{11 a}{52} + \frac{15}{2} \right)} + 1} + \frac{2 \cot{\left(a \right)}}{\cot^{2}{\left(a \right)} + 1}

   1                   2            
-------- + -------------------------
csc(2*a)      /a \    /      pi   a\
           csc|--|*csc|-15 + -- - -|
              \13/    \      2    2/

\frac{1}{\csc{\left(2 a \right)}} + \frac{2}{\csc{\left(\frac{a}{13} \right)} \csc{\left(- \frac{a}{2} - 15 + \frac{\pi}{2} \right)}}

                      /       2/  15   pi   a\\          
                      |    csc |- -- + -- - -||          
                      |        \  2    2    4/|          
                    4*|1 - -------------------|          
                      |           2/15   a\   |          
                      |        csc |-- + -|   |          
   1                  \            \2    4/   /          
-------- + ----------------------------------------------
csc(2*a)   /       2/  15   pi   a\\                     
           |    csc |- -- + -- - -||                     
           |        \  2    2    4/|    /a \    /pi   a \
           |1 + -------------------|*csc|--|*csc|-- - --|
           |           2/15   a\   |    \26/    \2    26/
           |        csc |-- + -|   |                     
           \            \2    4/   /

\frac{4 \left(1 - \frac{\csc^{2}{\left(- \frac{a}{4} - \frac{15}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}\right)}{\left(1 + \frac{\csc^{2}{\left(- \frac{a}{4} - \frac{15}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}\right) \csc{\left(\frac{a}{26} \right)} \csc{\left(- \frac{a}{26} + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(2 a \right)}}

                  /        2/15   a\\    /a \  
                4*|-1 + cot |-- + -||*cot|--|  
  2*cot(a)        \         \2    4//    \26/  
----------- + ---------------------------------
       2      /       2/a \\ /       2/15   a\\
1 + cot (a)   |1 + cot |--||*|1 + cot |-- + -||
              \        \26// \        \2    4//

\frac{2 \cot{\left(a \right)}}{\cot^{2}{\left(a \right)} + 1} + \frac{4 \left(\cot^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} - 1\right) \cot{\left(\frac{a}{26} \right)}}{\left(\cot^{2}{\left(\frac{a}{26} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1\right)}

         /15   11*a\                         /15   15*a\ 
    2*tan|-- + ----|                    2*tan|-- + ----| 
         \2     52 /      2*tan(a)           \2     52 / 
- ------------------- + ----------- + -------------------
         2/15   11*a\          2             2/15   15*a\
  1 + tan |-- + ----|   1 + tan (a)   1 + tan |-- + ----|
          \2     52 /                         \2     52 /

\frac{2 \tan{\left(\frac{15 a}{52} + \frac{15}{2} \right)}}{\tan^{2}{\left(\frac{15 a}{52} + \frac{15}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{11 a}{52} + \frac{15}{2} \right)}}{\tan^{2}{\left(\frac{11 a}{52} + \frac{15}{2} \right)} + 1} + \frac{2 \tan{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1}

                    /          4/30 + a\\           
                    |     8*sin |------||           
     2/a \    2/a \ |           \  4   /|           
8*cos |--|*sin |--|*|1 - ---------------|           
      \26/     \26/ \    1 - cos(30 + a)/           
----------------------------------------- + sin(2*a)
      /          4/30 + a\\                         
      |     8*sin |------||                         
      |           \  4   /|    /a \                 
      |1 + ---------------|*sin|--|                 
      \    1 - cos(30 + a)/    \13/

\frac{8 \left(1 - \frac{8 \sin^{4}{\left(\frac{a + 30}{4} \right)}}{1 - \cos{\left(a + 30 \right)}}\right) \sin^{2}{\left(\frac{a}{26} \right)} \cos^{2}{\left(\frac{a}{26} \right)}}{\left(1 + \frac{8 \sin^{4}{\left(\frac{a + 30}{4} \right)}}{1 - \cos{\left(a + 30 \right)}}\right) \sin{\left(\frac{a}{13} \right)}} + \sin{\left(2 a \right)}

                 2                                               
  /        2/a \\     4/a \ /       2/15   a\\    /a \           
4*|-1 + cot |--|| *sin |--|*|1 - tan |-- + -||*tan|--|           
  \         \52//      \52/ \        \2    4//    \26/           
------------------------------------------------------ + sin(2*a)
                          2/15   a\                              
                   1 + tan |-- + -|                              
                           \2    4/

\frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}\right) \left(\cot^{2}{\left(\frac{a}{52} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{a}{52} \right)} \tan{\left(\frac{a}{26} \right)}}{\tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1} + \sin{\left(2 a \right)}

      1                  1                     1         
------------- + ------------------- - -------------------
   /      pi\      /     pi   15*a\      /     pi   11*a\
sec|2*a - --|   sec|15 - -- + ----|   sec|15 - -- + ----|
   \      2 /      \     2     26 /      \     2     26 /

\frac{1}{\sec{\left(\frac{15 a}{26} - \frac{\pi}{2} + 15 \right)}} - \frac{1}{\sec{\left(\frac{11 a}{26} - \frac{\pi}{2} + 15 \right)}} + \frac{1}{\sec{\left(2 a - \frac{\pi}{2} \right)}}

     /     a\    /a \           
2*cos|15 + -|*sin|--| + sin(2*a)
     \     2/    \13/

2 \sin{\left(\frac{a}{13} \right)} \cos{\left(\frac{a}{2} + 15 \right)} + \sin{\left(2 a \right)}

  /       2/15   pi   a\\                                       
  |    cos |-- - -- + -||                                       
  |        \2    2    4/|    /a \    /  pi   a \                
4*|1 - -----------------|*cos|--|*cos|- -- + --|                
  |          2/15   a\  |    \26/    \  2    26/                
  |       cos |-- + -|  |                                       
  \           \2    4/  /                             /      pi\
------------------------------------------------ + cos|2*a - --|
                    2/15   pi   a\                    \      2 /
                 cos |-- - -- + -|                              
                     \2    2    4/                              
             1 + -----------------                              
                       2/15   a\                                
                    cos |-- + -|                                
                        \2    4/

\frac{4 \left(1 - \frac{\cos^{2}{\left(\frac{a}{4} - \frac{\pi}{2} + \frac{15}{2} \right)}}{\cos^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}\right) \cos{\left(\frac{a}{26} \right)} \cos{\left(\frac{a}{26} - \frac{\pi}{2} \right)}}{1 + \frac{\cos^{2}{\left(\frac{a}{4} - \frac{\pi}{2} + \frac{15}{2} \right)}}{\cos^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}} + \cos{\left(2 a - \frac{\pi}{2} \right)}

     /a \    /     pi   a\           
2*sin|--|*sin|15 + -- + -| + sin(2*a)
     \13/    \     2    2/

2 \sin{\left(\frac{a}{13} \right)} \sin{\left(\frac{a}{2} + \frac{\pi}{2} + 15 \right)} + \sin{\left(2 a \right)}

     2/a \ /       2/15   a\\    /a \           
4*cos |--|*|1 - tan |-- + -||*tan|--|           
      \26/ \        \2    4//    \26/           
------------------------------------- + sin(2*a)
                  2/15   a\                     
           1 + tan |-- + -|                     
                   \2    4/

\frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}\right) \cos^{2}{\left(\frac{a}{26} \right)} \tan{\left(\frac{a}{26} \right)}}{\tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1} + \sin{\left(2 a \right)}

4*cos(a/26)^2*(1 - tan(15/2 + a/4)^2)*tan(a/26)/(1 + tan(15/2 + a/4)^2) + sin(2*a)

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¿Cómo vas a descomponer esta sin(2a)-2sin(a/(2-15))*cos(a/2+15) expresión en fracciones?