Sr Examen

¿Cómo vas a descomponer esta sin(2*x)/((21*sin(x))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
 sin(2*x)
---------
21*sin(x)
$$\frac{\sin{\left(2 x \right)}}{21 \sin{\left(x \right)}}$$
sin(2*x)/((21*sin(x)))
Simplificación general [src]
2*cos(x)
--------
   21   
$$\frac{2 \cos{\left(x \right)}}{21}$$
2*cos(x)/21
Respuesta numérica [src]
0.0476190476190476*sin(2*x)/sin(x)
0.0476190476190476*sin(2*x)/sin(x)
Potencias [src]
    -2*I*x    2*I*x
 - e       + e     
-------------------
   /   -I*x    I*x\
21*\- e     + e   /
$$\frac{e^{2 i x} - e^{- 2 i x}}{21 \left(e^{i x} - e^{- i x}\right)}$$
(-exp(-2*i*x) + exp(2*i*x))/(21*(-exp(-i*x) + exp(i*x)))
Abrimos la expresión [src]
2*cos(x)
--------
   21   
$$\frac{2 \cos{\left(x \right)}}{21}$$
2*cos(x)/21
Parte trigonométrica [src]
      2       
--------------
      /pi    \
21*csc|-- - x|
      \2     /
$$\frac{2}{21 \csc{\left(- x + \frac{\pi}{2} \right)}}$$
     /    pi\
2*sin|x + --|
     \    2 /
-------------
      21     
$$\frac{2 \sin{\left(x + \frac{\pi}{2} \right)}}{21}$$
2*cos(x)
--------
   21   
$$\frac{2 \cos{\left(x \right)}}{21}$$
  /        2/x\\
2*|-1 + cot |-||
  \         \2//
----------------
   /       2/x\\
21*|1 + cot |-||
   \        \2//
$$\frac{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{21 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
   /      pi\ 
cos|2*x - --| 
   \      2 / 
--------------
      /    pi\
21*cos|x - --|
      \    2 /
$$\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{21 \cos{\left(x - \frac{\pi}{2} \right)}}$$
     /    pi\   
  sec|x - --|   
     \    2 /   
----------------
      /      pi\
21*sec|2*x - --|
      \      2 /
$$\frac{\sec{\left(x - \frac{\pi}{2} \right)}}{21 \sec{\left(2 x - \frac{\pi}{2} \right)}}$$
   csc(x)  
-----------
21*csc(2*x)
$$\frac{\csc{\left(x \right)}}{21 \csc{\left(2 x \right)}}$$
  /       2/x\\        
  |1 + tan |-||*tan(x) 
  \        \2//        
-----------------------
   /       2   \    /x\
21*\1 + tan (x)/*tan|-|
                    \2/
$$\frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(x \right)}}{21 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(\frac{x}{2} \right)}}$$
  /       2/x\\        
  |1 + cot |-||*cot(x) 
  \        \2//        
-----------------------
   /       2   \    /x\
21*\1 + cot (x)/*cot|-|
                    \2/
$$\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \cot{\left(x \right)}}{21 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}$$
  /       2/x\\ 
2*|1 - tan |-|| 
  \        \2// 
----------------
   /       2/x\\
21*|1 + tan |-||
   \        \2//
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{21 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
    2    
---------
21*sec(x)
$$\frac{2}{21 \sec{\left(x \right)}}$$
2/(21*sec(x))