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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(2*a)/((2*tg(a)))

¿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)
sin⁡(2a)2tan⁡(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)
sin⁡(2a)cos⁡(a)2sin⁡(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//
(1−tan⁡2(a2))2(tan⁡2(a2)+1)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(a)\cos^{2}{\left(a \right)} 
          /      pi\
cos(a)*cos|2*a - --|
          \      2 /
--------------------
        /    pi\    
   2*cos|a - --|    
        \    2 /
cos⁡(a)cos⁡(2a−π2)2cos⁡(a−π2)\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//
(cot⁡2(a2)−1)2(cot⁡2(a2)+1)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)
csc⁡(a)2csc⁡(2a)sec⁡(a)\frac{\csc{\left(a \right)}}{2 \csc{\left(2 a \right)} \sec{\left(a \right)}} 
   1   
-------
   2   
sec (a)
1sec⁡2(a)\frac{1}{\sec^{2}{\left(a \right)}} 
        /    pi\      
     sec|a - --|      
        \    2 /      
----------------------
            /      pi\
2*sec(a)*sec|2*a - --|
            \      2 /
sec⁡(a−π2)2sec⁡(a)sec⁡(2a−π2)\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)
cot⁡2(a)cot⁡2(a)+1\frac{\cot^{2}{\left(a \right)}}{\cot^{2}{\left(a \right)} + 1} 
   2     
sin (2*a)
---------
     2   
4*sin (a)
sin⁡2(2a)4sin⁡2(a)\frac{\sin^{2}{\left(2 a \right)}}{4 \sin^{2}{\left(a \right)}} 
     1      
------------
   2/pi    \
csc |-- - a|
    \2     /
1csc⁡2(−a+π2)\frac{1}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} 
     1     
-----------
       2   
1 + tan (a)
1tan⁡2(a)+1\frac{1}{\tan^{2}{\left(a \right)} + 1} 
        csc(a)        
----------------------
              /pi    \
2*csc(2*a)*csc|-- - a|
              \2     /
csc⁡(a)2csc⁡(2a)csc⁡(−a+π2)\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(a+π2)\sin^{2}{\left(a + \frac{\pi}{2} \right)} 
1   cos(2*a)
- + --------
2      2
cos⁡(2a)2+12\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)
sin⁡(a)cos⁡(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    /
−(eia+e−ia)(e2ia−e−2ia)4(−eia+e−ia)- \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)
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