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

Expresión a simplificar:

Solución

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