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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(5*pi/(2-a))^2

¿Cómo vas a descomponer esta tan(5*pi/(2-a))^2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   2/ 5*pi\
tan |-----|
    \2 - a/
tan⁡2(5π2−a)\tan^{2}{\left(\frac{5 \pi}{2 - a} \right)} 
tan((5*pi)/(2 - a))^2
Simplificación general [src] 
   2/ 5*pi \
tan |------|
    \-2 + a/
tan⁡2(5πa−2)\tan^{2}{\left(\frac{5 \pi}{a - 2} \right)} 
tan(5*pi/(-2 + a))^2
Respuesta numérica [src] 
tan((5*pi)/(2 - a))^2
tan((5*pi)/(2 - a))^2
Potencias [src] 
                       2 
 /   5*pi*I    -5*pi*I\  
 |   ------    -------|  
 |   2 - a      2 - a |  
-\- e       + e       /  
-------------------------
                      2  
  / -5*pi*I    5*pi*I\   
  | -------    ------|   
  |  2 - a     2 - a |   
  \e        + e      /
−(−e5iπ2−a+e−5iπ2−a)2(e5iπ2−a+e−5iπ2−a)2- \frac{\left(- e^{\frac{5 i \pi}{2 - a}} + e^{- \frac{5 i \pi}{2 - a}}\right)^{2}}{\left(e^{\frac{5 i \pi}{2 - a}} + e^{- \frac{5 i \pi}{2 - a}}\right)^{2}} 
-(-exp(5*pi*i/(2 - a)) + exp(-5*pi*i/(2 - a)))^2/(exp(-5*pi*i/(2 - a)) + exp(5*pi*i/(2 - a)))^2
Denominador racional [src] 
   2/ 5*pi \
tan |------|
    \-2 + a/
tan⁡2(5πa−2)\tan^{2}{\left(\frac{5 \pi}{a - 2} \right)} 
tan(5*pi/(-2 + a))^2
Parte trigonométrica [src] 
   2/pi    5*pi \
csc |-- - ------|
    \2    -2 + a/
-----------------
      2/ 5*pi \  
   csc |------|  
       \-2 + a/
csc⁡2(π2−5πa−2)csc⁡2(5πa−2)\frac{\csc^{2}{\left(\frac{\pi}{2} - \frac{5 \pi}{a - 2} \right)}}{\csc^{2}{\left(\frac{5 \pi}{a - 2} \right)}} 
     4/ 5*pi \
4*sin |------|
      \-2 + a/
--------------
    2/10*pi \ 
 sin |------| 
     \-2 + a/
4sin⁡4(5πa−2)sin⁡2(10πa−2)\frac{4 \sin^{4}{\left(\frac{5 \pi}{a - 2} \right)}}{\sin^{2}{\left(\frac{10 \pi}{a - 2} \right)}} 
   2/  pi    5*pi \
cos |- -- + ------|
    \  2    -2 + a/
-------------------
       2/ 5*pi \   
    cos |------|   
        \-2 + a/
cos⁡2(−π2+5πa−2)cos⁡2(5πa−2)\frac{\cos^{2}{\left(- \frac{\pi}{2} + \frac{5 \pi}{a - 2} \right)}}{\cos^{2}{\left(\frac{5 \pi}{a - 2} \right)}} 
       2/ 5*pi \   
    sec |------|   
        \-2 + a/   
-------------------
   2/  pi    5*pi \
sec |- -- + ------|
    \  2    -2 + a/
sec⁡2(5πa−2)sec⁡2(−π2+5πa−2)\frac{\sec^{2}{\left(\frac{5 \pi}{a - 2} \right)}}{\sec^{2}{\left(- \frac{\pi}{2} + \frac{5 \pi}{a - 2} \right)}} 
     4/ 5*pi\
4*sin |-----|
      \2 - a/
-------------
    2/10*pi\ 
 sin |-----| 
     \2 - a/
4sin⁡4(5π2−a)sin⁡2(10π2−a)\frac{4 \sin^{4}{\left(\frac{5 \pi}{2 - a} \right)}}{\sin^{2}{\left(\frac{10 \pi}{2 - a} \right)}} 
      2/ 5*pi\    
   sec |-----|    
       \2 - a/    
------------------
   2/  pi    5*pi\
sec |- -- + -----|
    \  2    2 - a/
sec⁡2(5π2−a)sec⁡2(−π2+5π2−a)\frac{\sec^{2}{\left(\frac{5 \pi}{2 - a} \right)}}{\sec^{2}{\left(- \frac{\pi}{2} + \frac{5 \pi}{2 - a} \right)}} 
     1     
-----------
   2/ 5*pi\
cot |-----|
    \2 - a/
1cot⁡2(5π2−a)\frac{1}{\cot^{2}{\left(\frac{5 \pi}{2 - a} \right)}} 
   2/  pi    5*pi\
cos |- -- + -----|
    \  2    2 - a/
------------------
      2/ 5*pi\    
   cos |-----|    
       \2 - a/
cos⁡2(−π2+5π2−a)cos⁡2(5π2−a)\frac{\cos^{2}{\left(- \frac{\pi}{2} + \frac{5 \pi}{2 - a} \right)}}{\cos^{2}{\left(\frac{5 \pi}{2 - a} \right)}} 
   2/ 5*pi\
sec |-----|
    \2 - a/
-----------
   2/ 5*pi\
csc |-----|
    \2 - a/
sec⁡2(5π2−a)csc⁡2(5π2−a)\frac{\sec^{2}{\left(\frac{5 \pi}{2 - a} \right)}}{\csc^{2}{\left(\frac{5 \pi}{2 - a} \right)}} 
   2/pi    5*pi\
csc |-- - -----|
    \2    2 - a/
----------------
     2/ 5*pi\   
  csc |-----|   
      \2 - a/
csc⁡2(π2−5π2−a)csc⁡2(5π2−a)\frac{\csc^{2}{\left(\frac{\pi}{2} - \frac{5 \pi}{2 - a} \right)}}{\csc^{2}{\left(\frac{5 \pi}{2 - a} \right)}} 
     1      
------------
   2/ 5*pi \
cot |------|
    \-2 + a/
1cot⁡2(5πa−2)\frac{1}{\cot^{2}{\left(\frac{5 \pi}{a - 2} \right)}} 
   2/ 5*pi \
tan |------|
    \-2 + a/
tan⁡2(5πa−2)\tan^{2}{\left(\frac{5 \pi}{a - 2} \right)} 
   2/ 5*pi\
sin |-----|
    \2 - a/
-----------
   2/ 5*pi\
cos |-----|
    \2 - a/
sin⁡2(5π2−a)cos⁡2(5π2−a)\frac{\sin^{2}{\left(\frac{5 \pi}{2 - a} \right)}}{\cos^{2}{\left(\frac{5 \pi}{2 - a} \right)}} 
sin(5*pi/(2 - a))^2/cos(5*pi/(2 - a))^2
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