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Simplificación de expresiones/ Descomposición en fracciones simples/ 3*sin(4*x)/(4*cos(4*x))

¿Cómo vas a descomponer esta 3*sin(4*x)/(4*cos(4*x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
3*sin(4*x)
----------
4*cos(4*x)
$$\frac{3 \sin{\left(4 x \right)}}{4 \cos{\left(4 x \right)}}$$ 
(3*sin(4*x))/((4*cos(4*x)))
Simplificación general [src] 
3*tan(4*x)
----------
    4
$$\frac{3 \tan{\left(4 x \right)}}{4}$$ 
3*tan(4*x)/4
Respuesta numérica [src] 
0.75*sin(4*x)/cos(4*x)
0.75*sin(4*x)/cos(4*x)
Potencias [src] 
     /   -4*I*x    4*I*x\
-3*I*\- e       + e     /
-------------------------
   /   -4*I*x      4*I*x\
 2*\2*e       + 2*e     /
$$- \frac{3 i \left(e^{4 i x} - e^{- 4 i x}\right)}{2 \left(2 e^{4 i x} + 2 e^{- 4 i x}\right)}$$ 
-3*i*(-exp(-4*i*x) + exp(4*i*x))/(2*(2*exp(-4*i*x) + 2*exp(4*i*x)))
Abrimos la expresión [src] 
            3                                          
       6*sin (x)*cos(x)            3*cos(x)*sin(x)     
- ------------------------- + -------------------------
           2           4               2           4   
  1 - 8*cos (x) + 8*cos (x)   1 - 8*cos (x) + 8*cos (x)
$$- \frac{6 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 8 \cos^{2}{\left(x \right)} + 1} + \frac{3 \sin{\left(x \right)} \cos{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 8 \cos^{2}{\left(x \right)} + 1}$$ 
-6*sin(x)^3*cos(x)/(1 - 8*cos(x)^2 + 8*cos(x)^4) + 3*cos(x)*sin(x)/(1 - 8*cos(x)^2 + 8*cos(x)^4)
Parte trigonométrica [src] 
    3     
----------
4*cot(4*x)
$$\frac{3}{4 \cot{\left(4 x \right)}}$$ 
    3*cot(2*x)    
------------------
  /        2     \
2*\-1 + cot (2*x)/
$$\frac{3 \cot{\left(2 x \right)}}{2 \left(\cot^{2}{\left(2 x \right)} - 1\right)}$$ 
3*sec(4*x)
----------
4*csc(4*x)
$$\frac{3 \sec{\left(4 x \right)}}{4 \csc{\left(4 x \right)}}$$ 
     /pi      \
3*csc|-- - 4*x|
     \2       /
---------------
   4*csc(4*x)
$$\frac{3 \csc{\left(- 4 x + \frac{\pi}{2} \right)}}{4 \csc{\left(4 x \right)}}$$ 
   3*sec(4*x)  
---------------
     /      pi\
4*sec|4*x - --|
     \      2 /
$$\frac{3 \sec{\left(4 x \right)}}{4 \sec{\left(4 x - \frac{\pi}{2} \right)}}$$ 
     /      pi\
3*cos|4*x - --|
     \      2 /
---------------
   4*cos(4*x)
$$\frac{3 \cos{\left(4 x - \frac{\pi}{2} \right)}}{4 \cos{\left(4 x \right)}}$$ 
   3*sin(4*x)  
---------------
     /pi      \
4*sin|-- + 4*x|
     \2       /
$$\frac{3 \sin{\left(4 x \right)}}{4 \sin{\left(4 x + \frac{\pi}{2} \right)}}$$ 
3*tan(4*x)
----------
    4
$$\frac{3 \tan{\left(4 x \right)}}{4}$$ 
    3*tan(2*x)   
-----------------
  /       2     \
2*\1 - tan (2*x)/
$$\frac{3 \tan{\left(2 x \right)}}{2 \left(1 - \tan^{2}{\left(2 x \right)}\right)}$$ 
     2     
3*sin (4*x)
-----------
 2*sin(8*x)
$$\frac{3 \sin^{2}{\left(4 x \right)}}{2 \sin{\left(8 x \right)}}$$ 
3*sin(4*x)^2/(2*sin(8*x))
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