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Simplificación de expresiones/ Descomposición en fracciones simples/ sin14*a/((2*cos7*a))

¿Cómo vas a descomponer esta sin14*a/((2*cos7*a)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
sin(14*a) 
----------
2*cos(7*a)
$$\frac{\sin{\left(14 a \right)}}{2 \cos{\left(7 a \right)}}$$ 
sin(14*a)/((2*cos(7*a)))
Simplificación general [src] 
sin(7*a)
$$\sin{\left(7 a \right)}$$ 
sin(7*a)
Abrimos la expresión [src] 
                         11                                                   7                                                    3                                                                                                         5                                                    13                                                    9                         
                12288*sin  (a)*cos(a)                                 7680*sin (a)*cos(a)                                   224*sin (a)*cos(a)                                    7*cos(a)*sin(a)                                    2016*sin (a)*cos(a)                                  4096*sin  (a)*cos(a)                                 14080*sin (a)*cos(a)               
- -------------------------------------------------- - -------------------------------------------------- - -------------------------------------------------- + -------------------------------------------------- + -------------------------------------------------- + -------------------------------------------------- + --------------------------------------------------
           5                       3            7               5                       3            7               5                       3            7               5                       3            7               5                       3            7               5                       3            7               5                       3            7   
  - 112*cos (a) - 7*cos(a) + 56*cos (a) + 64*cos (a)   - 112*cos (a) - 7*cos(a) + 56*cos (a) + 64*cos (a)   - 112*cos (a) - 7*cos(a) + 56*cos (a) + 64*cos (a)   - 112*cos (a) - 7*cos(a) + 56*cos (a) + 64*cos (a)   - 112*cos (a) - 7*cos(a) + 56*cos (a) + 64*cos (a)   - 112*cos (a) - 7*cos(a) + 56*cos (a) + 64*cos (a)   - 112*cos (a) - 7*cos(a) + 56*cos (a) + 64*cos (a)
$$\frac{4096 \sin^{13}{\left(a \right)} \cos{\left(a \right)}}{64 \cos^{7}{\left(a \right)} - 112 \cos^{5}{\left(a \right)} + 56 \cos^{3}{\left(a \right)} - 7 \cos{\left(a \right)}} - \frac{12288 \sin^{11}{\left(a \right)} \cos{\left(a \right)}}{64 \cos^{7}{\left(a \right)} - 112 \cos^{5}{\left(a \right)} + 56 \cos^{3}{\left(a \right)} - 7 \cos{\left(a \right)}} + \frac{14080 \sin^{9}{\left(a \right)} \cos{\left(a \right)}}{64 \cos^{7}{\left(a \right)} - 112 \cos^{5}{\left(a \right)} + 56 \cos^{3}{\left(a \right)} - 7 \cos{\left(a \right)}} - \frac{7680 \sin^{7}{\left(a \right)} \cos{\left(a \right)}}{64 \cos^{7}{\left(a \right)} - 112 \cos^{5}{\left(a \right)} + 56 \cos^{3}{\left(a \right)} - 7 \cos{\left(a \right)}} + \frac{2016 \sin^{5}{\left(a \right)} \cos{\left(a \right)}}{64 \cos^{7}{\left(a \right)} - 112 \cos^{5}{\left(a \right)} + 56 \cos^{3}{\left(a \right)} - 7 \cos{\left(a \right)}} - \frac{224 \sin^{3}{\left(a \right)} \cos{\left(a \right)}}{64 \cos^{7}{\left(a \right)} - 112 \cos^{5}{\left(a \right)} + 56 \cos^{3}{\left(a \right)} - 7 \cos{\left(a \right)}} + \frac{7 \sin{\left(a \right)} \cos{\left(a \right)}}{64 \cos^{7}{\left(a \right)} - 112 \cos^{5}{\left(a \right)} + 56 \cos^{3}{\left(a \right)} - 7 \cos{\left(a \right)}}$$ 
-12288*sin(a)^11*cos(a)/(-112*cos(a)^5 - 7*cos(a) + 56*cos(a)^3 + 64*cos(a)^7) - 7680*sin(a)^7*cos(a)/(-112*cos(a)^5 - 7*cos(a) + 56*cos(a)^3 + 64*cos(a)^7) - 224*sin(a)^3*cos(a)/(-112*cos(a)^5 - 7*cos(a) + 56*cos(a)^3 + 64*cos(a)^7) + 7*cos(a)*sin(a)/(-112*cos(a)^5 - 7*cos(a) + 56*cos(a)^3 + 64*cos(a)^7) + 2016*sin(a)^5*cos(a)/(-112*cos(a)^5 - 7*cos(a) + 56*cos(a)^3 + 64*cos(a)^7) + 4096*sin(a)^13*cos(a)/(-112*cos(a)^5 - 7*cos(a) + 56*cos(a)^3 + 64*cos(a)^7) + 14080*sin(a)^9*cos(a)/(-112*cos(a)^5 - 7*cos(a) + 56*cos(a)^3 + 64*cos(a)^7)
Parte trigonométrica [src] 
    /       2/7*a\\            
    |1 + tan |---||*tan(7*a)   
    \        \ 2 //            
-------------------------------
/       2     \ /       2/7*a\\
\1 + tan (7*a)/*|1 - tan |---||
                \        \ 2 //
$$\frac{\left(\tan^{2}{\left(\frac{7 a}{2} \right)} + 1\right) \tan{\left(7 a \right)}}{\left(1 - \tan^{2}{\left(\frac{7 a}{2} \right)}\right) \left(\tan^{2}{\left(7 a \right)} + 1\right)}$$ 
   /       pi\
cos|14*a - --|
   \       2 /
--------------
  2*cos(7*a)
$$\frac{\cos{\left(14 a - \frac{\pi}{2} \right)}}{2 \cos{\left(7 a \right)}}$$ 
   1    
--------
csc(7*a)
$$\frac{1}{\csc{\left(7 a \right)}}$$ 
  sec(7*a) 
-----------
2*csc(14*a)
$$\frac{\sec{\left(7 a \right)}}{2 \csc{\left(14 a \right)}}$$ 
      1      
-------------
   /      pi\
sec|7*a - --|
   \      2 /
$$\frac{1}{\sec{\left(7 a - \frac{\pi}{2} \right)}}$$ 
       /7*a\ 
  2*tan|---| 
       \ 2 / 
-------------
       2/7*a\
1 + tan |---|
        \ 2 /
$$\frac{2 \tan{\left(\frac{7 a}{2} \right)}}{\tan^{2}{\left(\frac{7 a}{2} \right)} + 1}$$ 
    /       2/7*a\\             
    |1 + cot |---||*cot(7*a)    
    \        \ 2 //             
--------------------------------
/       2     \ /        2/7*a\\
\1 + cot (7*a)/*|-1 + cot |---||
                \         \ 2 //
$$\frac{\left(\cot^{2}{\left(\frac{7 a}{2} \right)} + 1\right) \cot{\left(7 a \right)}}{\left(\cot^{2}{\left(\frac{7 a}{2} \right)} - 1\right) \left(\cot^{2}{\left(7 a \right)} + 1\right)}$$ 
       /7*a\ 
  2*cot|---| 
       \ 2 / 
-------------
       2/7*a\
1 + cot |---|
        \ 2 /
$$\frac{2 \cot{\left(\frac{7 a}{2} \right)}}{\cot^{2}{\left(\frac{7 a}{2} \right)} + 1}$$ 
    sec(7*a)    
----------------
     /       pi\
2*sec|14*a - --|
     \       2 /
$$\frac{\sec{\left(7 a \right)}}{2 \sec{\left(14 a - \frac{\pi}{2} \right)}}$$ 
sin(7*a)
$$\sin{\left(7 a \right)}$$ 
   /      pi\
cos|7*a - --|
   \      2 /
$$\cos{\left(7 a - \frac{\pi}{2} \right)}$$ 
   /pi      \
csc|-- - 7*a|
   \2       /
-------------
 2*csc(14*a)
$$\frac{\csc{\left(- 7 a + \frac{\pi}{2} \right)}}{2 \csc{\left(14 a \right)}}$$ 
   sin(14*a)   
---------------
     /pi      \
2*sin|-- + 7*a|
     \2       /
$$\frac{\sin{\left(14 a \right)}}{2 \sin{\left(7 a + \frac{\pi}{2} \right)}}$$ 
sin(14*a)/(2*sin(pi/2 + 7*a))
Respuesta numérica [src] 
0.5*sin(14*a)/cos(7*a)
0.5*sin(14*a)/cos(7*a)
Potencias [src] 
   /   -14*I*a    14*I*a\ 
-I*\- e        + e      / 
--------------------------
     / -7*I*a    7*I*a\   
   2*\e       + e     /
$$- \frac{i \left(e^{14 i a} - e^{- 14 i a}\right)}{2 \left(e^{7 i a} + e^{- 7 i a}\right)}$$ 
-i*(-exp(-14*i*a) + exp(14*i*a))/(2*(exp(-7*i*a) + exp(7*i*a)))
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