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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   /  pi \              
tan|-----| + 2*(-cot(a))
   \2 - a/
tan⁡(π2−a)+2(−cot⁡(a))\tan{\left(\frac{\pi}{2 - a} \right)} + 2 \left(- \cot{\left(a \right)}\right) 
tan(pi/(2 - a)) + 2*(-cot(a))
Simplificación general [src] 
     /  pi  \     2   
- tan|------| - ------
     \-2 + a/   tan(a)
−tan⁡(πa−2)−2tan⁡(a)- \tan{\left(\frac{\pi}{a - 2} \right)} - \frac{2}{\tan{\left(a \right)}} 
-tan(pi/(-2 + a)) - 2/tan(a)
Respuesta numérica [src] 
-2.0*cot(a) + tan(pi/(2 - a))
-2.0*cot(a) + tan(pi/(2 - a))
Combinatoria [src] 
               /  pi \
-2*cot(a) + tan|-----|
               \2 - a/
tan⁡(π2−a)−2cot⁡(a)\tan{\left(\frac{\pi}{2 - a} \right)} - 2 \cot{\left(a \right)} 
-2*cot(a) + tan(pi/(2 - a))
Unión de expresiones racionales [src] 
               /  pi \
-2*cot(a) + tan|-----|
               \2 - a/
tan⁡(π2−a)−2cot⁡(a)\tan{\left(\frac{\pi}{2 - a} \right)} - 2 \cot{\left(a \right)} 
-2*cot(a) + tan(pi/(2 - a))
Potencias [src] 
               /  pi \
-2*cot(a) + tan|-----|
               \2 - a/
tan⁡(π2−a)−2cot⁡(a)\tan{\left(\frac{\pi}{2 - a} \right)} - 2 \cot{\left(a \right)} 
              /    pi*I    -pi*I \
              |   -----    ------|
              |   2 - a    2 - a |
            I*\- e      + e      /
-2*cot(a) + ----------------------
                 pi*I    -pi*I    
                -----    ------   
                2 - a    2 - a    
               e      + e
i(−eiπ2−a+e−iπ2−a)eiπ2−a+e−iπ2−a−2cot⁡(a)\frac{i \left(- e^{\frac{i \pi}{2 - a}} + e^{- \frac{i \pi}{2 - a}}\right)}{e^{\frac{i \pi}{2 - a}} + e^{- \frac{i \pi}{2 - a}}} - 2 \cot{\left(a \right)} 
-2*cot(a) + i*(-exp(pi*i/(2 - a)) + exp(-pi*i/(2 - a)))/(exp(pi*i/(2 - a)) + exp(-pi*i/(2 - a)))
Denominador común [src] 
               /  pi \
-2*cot(a) + tan|-----|
               \2 - a/
tan⁡(π2−a)−2cot⁡(a)\tan{\left(\frac{\pi}{2 - a} \right)} - 2 \cot{\left(a \right)} 
-2*cot(a) + tan(pi/(2 - a))
Denominador racional [src] 
               /  pi \
-2*cot(a) + tan|-----|
               \2 - a/
tan⁡(π2−a)−2cot⁡(a)\tan{\left(\frac{\pi}{2 - a} \right)} - 2 \cot{\left(a \right)} 
-2*cot(a) + tan(pi/(2 - a))
Compilar la expresión [src] 
               /  pi \
-2*cot(a) + tan|-----|
               \2 - a/
tan⁡(π2−a)−2cot⁡(a)\tan{\left(\frac{\pi}{2 - a} \right)} - 2 \cot{\left(a \right)} 
-2*cot(a) + tan(pi/(2 - a))
Parte trigonométrica [src] 
   /  pi \           
sec|-----|           
   \2 - a/   2*csc(a)
---------- - --------
   /  pi \    sec(a) 
csc|-----|           
   \2 - a/
−2csc⁡(a)sec⁡(a)+sec⁡(π2−a)csc⁡(π2−a)- \frac{2 \csc{\left(a \right)}}{\sec{\left(a \right)}} + \frac{\sec{\left(\frac{\pi}{2 - a} \right)}}{\csc{\left(\frac{\pi}{2 - a} \right)}} 
   /pi     pi \              
csc|-- - -----|              
   \2    2 - a/     2*csc(a) 
--------------- - -----------
      /  pi \        /pi    \
   csc|-----|     csc|-- - a|
      \2 - a/        \2     /
−2csc⁡(a)csc⁡(−a+π2)+csc⁡(π2−π2−a)csc⁡(π2−a)- \frac{2 \csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{\csc{\left(\frac{\pi}{2} - \frac{\pi}{2 - a} \right)}}{\csc{\left(\frac{\pi}{2 - a} \right)}} 
   /  pi \           
sin|-----|           
   \2 - a/   2*cos(a)
---------- - --------
   /  pi \    sin(a) 
cos|-----|           
   \2 - a/
sin⁡(π2−a)cos⁡(π2−a)−2cos⁡(a)sin⁡(a)\frac{\sin{\left(\frac{\pi}{2 - a} \right)}}{\cos{\left(\frac{\pi}{2 - a} \right)}} - \frac{2 \cos{\left(a \right)}}{\sin{\left(a \right)}} 
     /pi     pi  \              
  csc|-- - ------|              
     \2    -2 + a/     2*csc(a) 
- ---------------- - -----------
       /  pi  \         /pi    \
    csc|------|      csc|-- - a|
       \-2 + a/         \2     /
−2csc⁡(a)csc⁡(−a+π2)−csc⁡(π2−πa−2)csc⁡(πa−2)- \frac{2 \csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} - \frac{\csc{\left(\frac{\pi}{2} - \frac{\pi}{a - 2} \right)}}{\csc{\left(\frac{\pi}{a - 2} \right)}} 
               /  pi \
-2*cot(a) + tan|-----|
               \2 - a/
tan⁡(π2−a)−2cot⁡(a)\tan{\left(\frac{\pi}{2 - a} \right)} - 2 \cot{\left(a \right)} 
       /  pi \           /    pi\
    sec|-----|      2*sec|a - --|
       \2 - a/           \    2 /
----------------- - -------------
   /  pi     pi \       sec(a)   
sec|- -- + -----|                
   \  2    2 - a/
sec⁡(π2−a)sec⁡(−π2+π2−a)−2sec⁡(a−π2)sec⁡(a)\frac{\sec{\left(\frac{\pi}{2 - a} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{\pi}{2 - a} \right)}} - \frac{2 \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}} 
     /  pi     pi  \              
  cos|- -- + ------|              
     \  2    -2 + a/     2*cos(a) 
- ------------------ - -----------
        /  pi  \          /    pi\
     cos|------|       cos|a - --|
        \-2 + a/          \    2 /
−2cos⁡(a)cos⁡(a−π2)−cos⁡(−π2+πa−2)cos⁡(πa−2)- \frac{2 \cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} - \frac{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)}}{\cos{\left(\frac{\pi}{a - 2} \right)}} 
       1                
- ----------- - 2*cot(a)
     /  pi  \           
  cot|------|           
     \-2 + a/
−2cot⁡(a)−1cot⁡(πa−2)- 2 \cot{\left(a \right)} - \frac{1}{\cot{\left(\frac{\pi}{a - 2} \right)}} 
    1                
---------- - 2*cot(a)
   /  pi \           
cot|-----|           
   \2 - a/
−2cot⁡(a)+1cot⁡(π2−a)- 2 \cot{\left(a \right)} + \frac{1}{\cot{\left(\frac{\pi}{2 - a} \right)}} 
        /  pi  \            /    pi\
     sec|------|       2*sec|a - --|
        \-2 + a/            \    2 /
- ------------------ - -------------
     /  pi     pi  \       sec(a)   
  sec|- -- + ------|                
     \  2    -2 + a/
−sec⁡(πa−2)sec⁡(−π2+πa−2)−2sec⁡(a−π2)sec⁡(a)- \frac{\sec{\left(\frac{\pi}{a - 2} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)}} - \frac{2 \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}} 
     /  pi  \     2   
- tan|------| - ------
     \-2 + a/   tan(a)
−tan⁡(πa−2)−2tan⁡(a)- \tan{\left(\frac{\pi}{a - 2} \right)} - \frac{2}{\tan{\left(a \right)}} 
                  2/  pi  \
             2*sin |------|
  sin(2*a)         \-2 + a/
- -------- - --------------
     2           / 2*pi \  
  sin (a)     sin|------|  
                 \-2 + a/
−2sin⁡2(πa−2)sin⁡(2πa−2)−sin⁡(2a)sin⁡2(a)- \frac{2 \sin^{2}{\left(\frac{\pi}{a - 2} \right)}}{\sin{\left(\frac{2 \pi}{a - 2} \right)}} - \frac{\sin{\left(2 a \right)}}{\sin^{2}{\left(a \right)}} 
   /  pi     pi \              
cos|- -- + -----|              
   \  2    2 - a/     2*cos(a) 
----------------- - -----------
       /  pi \         /    pi\
    cos|-----|      cos|a - --|
       \2 - a/         \    2 /
−2cos⁡(a)cos⁡(a−π2)+cos⁡(−π2+π2−a)cos⁡(π2−a)- \frac{2 \cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} + \frac{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{2 - a} \right)}}{\cos{\left(\frac{\pi}{2 - a} \right)}} 
    2         /  pi \
- ------ + tan|-----|
  tan(a)      \2 - a/
tan⁡(π2−a)−2tan⁡(a)\tan{\left(\frac{\pi}{2 - a} \right)} - \frac{2}{\tan{\left(a \right)}} 
                  2/  pi \
             2*sin |-----|
  sin(2*a)         \2 - a/
- -------- + -------------
     2            / 2*pi\ 
  sin (a)      sin|-----| 
                  \2 - a/
2sin⁡2(π2−a)sin⁡(2π2−a)−sin⁡(2a)sin⁡2(a)\frac{2 \sin^{2}{\left(\frac{\pi}{2 - a} \right)}}{\sin{\left(\frac{2 \pi}{2 - a} \right)}} - \frac{\sin{\left(2 a \right)}}{\sin^{2}{\left(a \right)}} 
-sin(2*a)/sin(a)^2 + 2*sin(pi/(2 - a))^2/sin(2*pi/(2 - a))
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