Sr Examen

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

Expresión a simplificar:

Solución

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