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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(4*x)/(4*cos(4*x))

¿Cómo vas a descomponer esta sin(4*x)/(4*cos(4*x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
 sin(4*x) 
----------
4*cos(4*x)
$$\frac{\sin{\left(4 x \right)}}{4 \cos{\left(4 x \right)}}$$ 
sin(4*x)/((4*cos(4*x)))
Simplificación general [src] 
tan(4*x)
--------
   4
$$\frac{\tan{\left(4 x \right)}}{4}$$ 
tan(4*x)/4
Abrimos la expresión [src] 
                                      3              
      cos(x)*sin(x)              2*sin (x)*cos(x)    
------------------------- - -------------------------
         2           4               2           4   
1 - 8*cos (x) + 8*cos (x)   1 - 8*cos (x) + 8*cos (x)
$$- \frac{2 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 8 \cos^{2}{\left(x \right)} + 1} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 8 \cos^{2}{\left(x \right)} + 1}$$ 
cos(x)*sin(x)/(1 - 8*cos(x)^2 + 8*cos(x)^4) - 2*sin(x)^3*cos(x)/(1 - 8*cos(x)^2 + 8*cos(x)^4)
Parte trigonométrica [src] 
    1     
----------
4*cot(4*x)
$$\frac{1}{4 \cot{\left(4 x \right)}}$$ 
    sin(4*x)   
---------------
     /pi      \
4*sin|-- + 4*x|
     \2       /
$$\frac{\sin{\left(4 x \right)}}{4 \sin{\left(4 x + \frac{\pi}{2} \right)}}$$ 
    sec(4*x)   
---------------
     /      pi\
4*sec|4*x - --|
     \      2 /
$$\frac{\sec{\left(4 x \right)}}{4 \sec{\left(4 x - \frac{\pi}{2} \right)}}$$ 
   /      pi\
cos|4*x - --|
   \      2 /
-------------
  4*cos(4*x)
$$\frac{\cos{\left(4 x - \frac{\pi}{2} \right)}}{4 \cos{\left(4 x \right)}}$$ 
     tan(2*x)    
-----------------
  /       2     \
2*\1 - tan (2*x)/
$$\frac{\tan{\left(2 x \right)}}{2 \left(1 - \tan^{2}{\left(2 x \right)}\right)}$$ 
 sec(4*x) 
----------
4*csc(4*x)
$$\frac{\sec{\left(4 x \right)}}{4 \csc{\left(4 x \right)}}$$ 
   /pi      \
csc|-- - 4*x|
   \2       /
-------------
  4*csc(4*x)
$$\frac{\csc{\left(- 4 x + \frac{\pi}{2} \right)}}{4 \csc{\left(4 x \right)}}$$ 
   2      
sin (4*x) 
----------
2*sin(8*x)
$$\frac{\sin^{2}{\left(4 x \right)}}{2 \sin{\left(8 x \right)}}$$ 
tan(4*x)
--------
   4
$$\frac{\tan{\left(4 x \right)}}{4}$$ 
     cot(2*x)     
------------------
  /        2     \
2*\-1 + cot (2*x)/
$$\frac{\cot{\left(2 x \right)}}{2 \left(\cot^{2}{\left(2 x \right)} - 1\right)}$$ 
cot(2*x)/(2*(-1 + cot(2*x)^2))
Respuesta numérica [src] 
0.25*sin(4*x)/cos(4*x)
0.25*sin(4*x)/cos(4*x)
Potencias [src] 
   /   -4*I*x    4*I*x\ 
-I*\- e       + e     / 
------------------------
  /   -4*I*x      4*I*x\
2*\2*e       + 2*e     /
$$- \frac{i \left(e^{4 i x} - e^{- 4 i x}\right)}{2 \left(2 e^{4 i x} + 2 e^{- 4 i x}\right)}$$ 
-i*(-exp(-4*i*x) + exp(4*i*x))/(2*(2*exp(-4*i*x) + 2*exp(4*i*x)))
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