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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(3*pi/(2-a))-(-1)*cos(a)

¿Cómo vas a descomponer esta sin(3*pi/(2-a))-(-1)*cos(a) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   / 3*pi\         
sin|-----| + cos(a)
   \2 - a/
sin⁡(3π2−a)+cos⁡(a)\sin{\left(\frac{3 \pi}{2 - a} \right)} + \cos{\left(a \right)} 
sin((3*pi)/(2 - a)) + cos(a)
Simplificación general [src] 
     / 3*pi \         
- sin|------| + cos(a)
     \-2 + a/
−sin⁡(3πa−2)+cos⁡(a)- \sin{\left(\frac{3 \pi}{a - 2} \right)} + \cos{\left(a \right)} 
-sin(3*pi/(-2 + a)) + cos(a)
Respuesta numérica [src] 
cos(a) + sin((3*pi)/(2 - a))
cos(a) + sin((3*pi)/(2 - a))
Denominador racional [src] 
     / 3*pi \         
- sin|------| + cos(a)
     \-2 + a/
−sin⁡(3πa−2)+cos⁡(a)- \sin{\left(\frac{3 \pi}{a - 2} \right)} + \cos{\left(a \right)} 
-sin(3*pi/(-2 + a)) + cos(a)
Parte trigonométrica [src] 
       2/a\         /   3*pi   \  
1 - tan |-|    2*tan|----------|  
        \2/         \2*(-2 + a)/  
----------- - --------------------
       2/a\          2/   3*pi   \
1 + tan |-|   1 + tan |----------|
        \2/           \2*(-2 + a)/
1−tan⁡2(a2)tan⁡2(a2)+1−2tan⁡(3π2(a−2))tan⁡2(3π2(a−2))+1\frac{1 - \tan^{2}{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{3 \pi}{2 \left(a - 2\right)} \right)}}{\tan^{2}{\left(\frac{3 \pi}{2 \left(a - 2\right)} \right)} + 1} 
       2/a\          /   3*pi  \ 
1 - tan |-|     2*tan|---------| 
        \2/          \2*(2 - a)/ 
----------- + -------------------
       2/a\          2/   3*pi  \
1 + tan |-|   1 + tan |---------|
        \2/           \2*(2 - a)/
1−tan⁡2(a2)tan⁡2(a2)+1+2tan⁡(3π2(2−a))tan⁡2(3π2(2−a))+1\frac{1 - \tan^{2}{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{3 \pi}{2 \left(2 - a\right)} \right)}}{\tan^{2}{\left(\frac{3 \pi}{2 \left(2 - a\right)} \right)} + 1} 
     / 3*pi \         
- sin|------| + cos(a)
     \-2 + a/
−sin⁡(3πa−2)+cos⁡(a)- \sin{\left(\frac{3 \pi}{a - 2} \right)} + \cos{\left(a \right)} 
     1             1     
----------- - -----------
   /pi    \      / 3*pi \
csc|-- - a|   csc|------|
   \2     /      \-2 + a/
1csc⁡(−a+π2)−1csc⁡(3πa−2)\frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(\frac{3 \pi}{a - 2} \right)}} 
  1              1         
------ - ------------------
sec(a)      /  pi    3*pi \
         sec|- -- + ------|
            \  2    -2 + a/
−1sec⁡(−π2+3πa−2)+1sec⁡(a)- \frac{1}{\sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a - 2} \right)}} + \frac{1}{\sec{\left(a \right)}} 
        2/a\          /   3*pi  \ 
-1 + cot |-|     2*cot|---------| 
         \2/          \2*(2 - a)/ 
------------ + -------------------
       2/a\           2/   3*pi  \
1 + cot |-|    1 + cot |---------|
        \2/            \2*(2 - a)/
cot⁡2(a2)−1cot⁡2(a2)+1+2cot⁡(3π2(2−a))cot⁡2(3π2(2−a))+1\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{2 \cot{\left(\frac{3 \pi}{2 \left(2 - a\right)} \right)}}{\cot^{2}{\left(\frac{3 \pi}{2 \left(2 - a\right)} \right)} + 1} 
    1             1     
---------- + -----------
   / 3*pi\      /pi    \
csc|-----|   csc|-- - a|
   \2 - a/      \2     /
1csc⁡(−a+π2)+1csc⁡(3π2−a)\frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(\frac{3 \pi}{2 - a} \right)}} 
            /  pi    3*pi\
cos(a) + cos|- -- + -----|
            \  2    2 - a/
cos⁡(a)+cos⁡(−π2+3π2−a)\cos{\left(a \right)} + \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{2 - a} \right)} 
        2/a\         /   3*pi   \  
-1 + cot |-|    2*cot|----------|  
         \2/         \2*(-2 + a)/  
------------ - --------------------
       2/a\           2/   3*pi   \
1 + cot |-|    1 + cot |----------|
        \2/            \2*(-2 + a)/
cot⁡2(a2)−1cot⁡2(a2)+1−2cot⁡(3π2(a−2))cot⁡2(3π2(a−2))+1\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} - \frac{2 \cot{\left(\frac{3 \pi}{2 \left(a - 2\right)} \right)}}{\cot^{2}{\left(\frac{3 \pi}{2 \left(a - 2\right)} \right)} + 1} 
    1          1   
---------- + ------
   / 3*pi\   sec(a)
csc|-----|         
   \2 - a/
1sec⁡(a)+1csc⁡(3π2−a)\frac{1}{\sec{\left(a \right)}} + \frac{1}{\csc{\left(\frac{3 \pi}{2 - a} \right)}} 
   / 3*pi\      /    pi\
sin|-----| + sin|a + --|
   \2 - a/      \    2 /
sin⁡(3π2−a)+sin⁡(a+π2)\sin{\left(\frac{3 \pi}{2 - a} \right)} + \sin{\left(a + \frac{\pi}{2} \right)} 
     /  pi    3*pi \         
- cos|- -- + ------| + cos(a)
     \  2    -2 + a/
cos⁡(a)−cos⁡(−π2+3πa−2)\cos{\left(a \right)} - \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a - 2} \right)} 
  1              1        
------ + -----------------
sec(a)      /  pi    3*pi\
         sec|- -- + -----|
            \  2    2 - a/
1sec⁡(−π2+3π2−a)+1sec⁡(a)\frac{1}{\sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{2 - a} \right)}} + \frac{1}{\sec{\left(a \right)}} 
     / 3*pi \      /    pi\
- sin|------| + sin|a + --|
     \-2 + a/      \    2 /
−sin⁡(3πa−2)+sin⁡(a+π2)- \sin{\left(\frac{3 \pi}{a - 2} \right)} + \sin{\left(a + \frac{\pi}{2} \right)} 
-sin(3*pi/(-2 + a)) + sin(a + pi/2)
Potencias [src] 
                 /   -3*pi*I    3*pi*I\
                 |   -------    ------|
 I*a    -I*a     |    2 - a     2 - a |
e      e       I*\- e        + e      /
---- + ----- - ------------------------
 2       2                2
−i(e3iπ2−a−e−3iπ2−a)2+eia2+e−ia2- \frac{i \left(e^{\frac{3 i \pi}{2 - a}} - e^{- \frac{3 i \pi}{2 - a}}\right)}{2} + \frac{e^{i a}}{2} + \frac{e^{- i a}}{2} 
exp(i*a)/2 + exp(-i*a)/2 - i*(-exp(-3*pi*i/(2 - a)) + exp(3*pi*i/(2 - a)))/2
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