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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(п+a)*ctg(п-a)/(п/2-a)

¿Cómo vas a descomponer esta sin(п+a)*ctg(п-a)/(п/2-a) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
sin(pi + a)*cot(pi - a)
-----------------------
         pi            
         -- - a        
         2
sin⁡(a+π)cot⁡(π−a)−a+π2\frac{\sin{\left(a + \pi \right)} \cot{\left(\pi - a \right)}}{- a + \frac{\pi}{2}} 
(sin(pi + a)*cot(pi - a))/(pi/2 - a)
Simplificación general [src] 
-2*cos(a)
---------
-pi + 2*a
−2cos⁡(a)2a−π- \frac{2 \cos{\left(a \right)}}{2 a - \pi} 
-2*cos(a)/(-pi + 2*a)
Respuesta numérica [src] 
cot(pi - a)*sin(pi + a)/(1.5707963267949 - a)
cot(pi - a)*sin(pi + a)/(1.5707963267949 - a)
Potencias [src] 
cot(a)*sin(a)
-------------
    pi       
    -- - a   
    2
sin⁡(a)cot⁡(a)−a+π2\frac{\sin{\left(a \right)} \cot{\left(a \right)}}{- a + \frac{\pi}{2}} 
  /   I*(-pi - a)    I*(pi + a)\       
I*\- e            + e          /*cot(a)
---------------------------------------
                 /pi    \              
               2*|-- - a|              
                 \2     /
i(−ei(−a−π)+ei(a+π))cot⁡(a)2(−a+π2)\frac{i \left(- e^{i \left(- a - \pi\right)} + e^{i \left(a + \pi\right)}\right) \cot{\left(a \right)}}{2 \left(- a + \frac{\pi}{2}\right)} 
i*(-exp(i*(-pi - a)) + exp(i*(pi + a)))*cot(a)/(2*(pi/2 - a))
Denominador común [src] 
-2*cot(pi - a)*sin(pi + a)
--------------------------
        -pi + 2*a
−2sin⁡(a+π)cot⁡(π−a)2a−π- \frac{2 \sin{\left(a + \pi \right)} \cot{\left(\pi - a \right)}}{2 a - \pi} 
-2*cot(pi - a)*sin(pi + a)/(-pi + 2*a)
Denominador racional [src] 
-2*cot(a)*sin(a)
----------------
   -pi + 2*a
−2sin⁡(a)cot⁡(a)2a−π- \frac{2 \sin{\left(a \right)} \cot{\left(a \right)}}{2 a - \pi} 
-2*cot(a)*sin(a)/(-pi + 2*a)
Unión de expresiones racionales [src] 
2*cot(a)*sin(a)
---------------
    pi - 2*a
2sin⁡(a)cot⁡(a)π−2a\frac{2 \sin{\left(a \right)} \cot{\left(a \right)}}{\pi - 2 a} 
2*cot(a)*sin(a)/(pi - 2*a)
Parte trigonométrica [src] 
           2*cot(a)          
-----------------------------
/       1   \ /pi    \    /a\
|1 + -------|*|-- - a|*cot|-|
|       2/a\| \2     /    \2/
|    cot |-||                
\        \2//
2cot⁡(a)(1+1cot⁡2(a2))(−a+π2)cot⁡(a2)\frac{2 \cot{\left(a \right)}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \left(- a + \frac{\pi}{2}\right) \cot{\left(\frac{a}{2} \right)}} 
       1       
---------------
/pi    \       
|-- - a|*sec(a)
\2     /
1(−a+π2)sec⁡(a)\frac{1}{\left(- a + \frac{\pi}{2}\right) \sec{\left(a \right)}} 
               /a\    
   2*cot(a)*tan|-|    
               \2/    
----------------------
/       2/a\\ /pi    \
|1 + tan |-||*|-- - a|
\        \2// \2     /
2tan⁡(a2)cot⁡(a)(−a+π2)(tan⁡2(a2)+1)\frac{2 \tan{\left(\frac{a}{2} \right)} \cot{\left(a \right)}}{\left(- a + \frac{\pi}{2}\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)} 
                /a\          
           2*cot|-|          
                \2/          
-----------------------------
/       2/a\\ /pi    \       
|1 + cot |-||*|-- - a|*tan(a)
\        \2// \2     /
2cot⁡(a2)(−a+π2)(cot⁡2(a2)+1)tan⁡(a)\frac{2 \cot{\left(\frac{a}{2} \right)}}{\left(- a + \frac{\pi}{2}\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(a \right)}} 
         1          
--------------------
/pi    \    /pi    \
|-- - a|*csc|-- - a|
\2     /    \2     /
1(−a+π2)csc⁡(−a+π2)\frac{1}{\left(- a + \frac{\pi}{2}\right) \csc{\left(- a + \frac{\pi}{2} \right)}} 
            2/a\      
     1 - tan |-|      
             \2/      
----------------------
/       2/a\\ /pi    \
|1 + tan |-||*|-- - a|
\        \2// \2     /
1−tan⁡2(a2)(−a+π2)(tan⁡2(a2)+1)\frac{1 - \tan^{2}{\left(\frac{a}{2} \right)}}{\left(- a + \frac{\pi}{2}\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)} 
           /    pi\        
       -sec|a - --|        
           \    2 /        
---------------------------
/pi    \           /    pi\
|-- - a|*sec(a)*sec|a + --|
\2     /           \    2 /
−sec⁡(a−π2)(−a+π2)sec⁡(a)sec⁡(a+π2)- \frac{\sec{\left(a - \frac{\pi}{2} \right)}}{\left(- a + \frac{\pi}{2}\right) \sec{\left(a \right)} \sec{\left(a + \frac{\pi}{2} \right)}} 
                 2                  
------------------------------------
/       1   \ /pi    \           /a\
|1 + -------|*|-- - a|*tan(a)*tan|-|
|       2/a\| \2     /           \2/
|    tan |-||                       
\        \2//
2(1+1tan⁡2(a2))(−a+π2)tan⁡(a2)tan⁡(a)\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(- a + \frac{\pi}{2}\right) \tan{\left(\frac{a}{2} \right)} \tan{\left(a \right)}} 
cos(a)
------
pi    
-- - a
2
cos⁡(a)−a+π2\frac{\cos{\left(a \right)}}{- a + \frac{\pi}{2}} 
   /    pi\
sin|a + --|
   \    2 /
-----------
   pi      
   -- - a  
   2
sin⁡(a+π2)−a+π2\frac{\sin{\left(a + \frac{\pi}{2} \right)}}{- a + \frac{\pi}{2}} 
     sin(2*a)    
-----------------
  /pi    \       
2*|-- - a|*sin(a)
  \2     /
sin⁡(2a)2(−a+π2)sin⁡(a)\frac{\sin{\left(2 a \right)}}{2 \left(- a + \frac{\pi}{2}\right) \sin{\left(a \right)}} 
           /    pi\ 
-cos(a)*cos|a + --| 
           \    2 / 
--------------------
/pi    \    /pi    \
|-- - a|*cos|-- - a|
\2     /    \2     /
−cos⁡(a)cos⁡(a+π2)(−a+π2)cos⁡(−a+π2)- \frac{\cos{\left(a \right)} \cos{\left(a + \frac{\pi}{2} \right)}}{\left(- a + \frac{\pi}{2}\right) \cos{\left(- a + \frac{\pi}{2} \right)}} 
             2/a\     
     -1 + cot |-|     
              \2/     
----------------------
/       2/a\\ /pi    \
|1 + cot |-||*|-- - a|
\        \2// \2     /
cot⁡2(a2)−1(−a+π2)(cot⁡2(a2)+1)\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\left(- a + \frac{\pi}{2}\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)} 
(-1 + cot(a/2)^2)/((1 + cot(a/2)^2)*(pi/2 - a))
Combinatoria [src] 
-2*cot(a)*sin(a)
----------------
   -pi + 2*a
−2sin⁡(a)cot⁡(a)2a−π- \frac{2 \sin{\left(a \right)} \cot{\left(a \right)}}{2 a - \pi} 
-2*cot(a)*sin(a)/(-pi + 2*a)
Abrimos la expresión [src] 
              sin(a)                         zoo*cot(a)*sin(a)         
---------------------------------- + ----------------------------------
                         pi*cot(a)                            pi*cot(a)
zoo + a*cot(a) + zoo*a - ---------   zoo + a*cot(a) + zoo*a - ---------
                             2                                    2
∞~sin⁡(a)cot⁡(a)acot⁡(a)+∞~a−πcot⁡(a)2+∞~+sin⁡(a)acot⁡(a)+∞~a−πcot⁡(a)2+∞~\frac{\tilde{\infty} \sin{\left(a \right)} \cot{\left(a \right)}}{a \cot{\left(a \right)} + \tilde{\infty} a - \frac{\pi \cot{\left(a \right)}}{2} + \tilde{\infty}} + \frac{\sin{\left(a \right)}}{a \cot{\left(a \right)} + \tilde{\infty} a - \frac{\pi \cot{\left(a \right)}}{2} + \tilde{\infty}} 
sin(a)/(±oo + a*cot(a) + ±oo*a - pi*cot(a)/2) + ±oo*cot(a)*sin(a)/(±oo + a*cot(a) + ±oo*a - pi*cot(a)/2)
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