Sr Examen

Otras calculadoras

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/
$$\sin{\left(\frac{3 \pi}{2 - a} \right)} + \cos{\left(a \right)}$$ 
sin((3*pi)/(2 - a)) + cos(a)
Simplificación general [src] 
     / 3*pi \         
- sin|------| + cos(a)
     \-2 + a/
$$- \sin{\left(\frac{3 \pi}{a - 2} \right)} + \cos{\left(a \right)}$$ 
-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/
$$- \sin{\left(\frac{3 \pi}{a - 2} \right)} + \cos{\left(a \right)}$$ 
-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)/
$$\frac{1 - \tan^{2}{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{3 \pi}{2 \left(a - 2\right)} \right)}}{\tan^{2}{\left(\frac{3 \pi}{2 \left(a - 2\right)} \right)} + 1}$$ 
       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)/
$$\frac{1 - \tan^{2}{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{3 \pi}{2 \left(2 - a\right)} \right)}}{\tan^{2}{\left(\frac{3 \pi}{2 \left(2 - a\right)} \right)} + 1}$$ 
     / 3*pi \         
- sin|------| + cos(a)
     \-2 + a/
$$- \sin{\left(\frac{3 \pi}{a - 2} \right)} + \cos{\left(a \right)}$$ 
     1             1     
----------- - -----------
   /pi    \      / 3*pi \
csc|-- - a|   csc|------|
   \2     /      \-2 + a/
$$\frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(\frac{3 \pi}{a - 2} \right)}}$$ 
  1              1         
------ - ------------------
sec(a)      /  pi    3*pi \
         sec|- -- + ------|
            \  2    -2 + a/
$$- \frac{1}{\sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a - 2} \right)}} + \frac{1}{\sec{\left(a \right)}}$$ 
        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)/
$$\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{2 \cot{\left(\frac{3 \pi}{2 \left(2 - a\right)} \right)}}{\cot^{2}{\left(\frac{3 \pi}{2 \left(2 - a\right)} \right)} + 1}$$ 
    1             1     
---------- + -----------
   / 3*pi\      /pi    \
csc|-----|   csc|-- - a|
   \2 - a/      \2     /
$$\frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(\frac{3 \pi}{2 - a} \right)}}$$ 
            /  pi    3*pi\
cos(a) + cos|- -- + -----|
            \  2    2 - a/
$$\cos{\left(a \right)} + \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{2 - a} \right)}$$ 
        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)/
$$\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} - \frac{2 \cot{\left(\frac{3 \pi}{2 \left(a - 2\right)} \right)}}{\cot^{2}{\left(\frac{3 \pi}{2 \left(a - 2\right)} \right)} + 1}$$ 
    1          1   
---------- + ------
   / 3*pi\   sec(a)
csc|-----|         
   \2 - a/
$$\frac{1}{\sec{\left(a \right)}} + \frac{1}{\csc{\left(\frac{3 \pi}{2 - a} \right)}}$$ 
   / 3*pi\      /    pi\
sin|-----| + sin|a + --|
   \2 - a/      \    2 /
$$\sin{\left(\frac{3 \pi}{2 - a} \right)} + \sin{\left(a + \frac{\pi}{2} \right)}$$ 
     /  pi    3*pi \         
- cos|- -- + ------| + cos(a)
     \  2    -2 + a/
$$\cos{\left(a \right)} - \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a - 2} \right)}$$ 
  1              1        
------ + -----------------
sec(a)      /  pi    3*pi\
         sec|- -- + -----|
            \  2    2 - a/
$$\frac{1}{\sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{2 - a} \right)}} + \frac{1}{\sec{\left(a \right)}}$$ 
     / 3*pi \      /    pi\
- sin|------| + sin|a + --|
     \-2 + a/      \    2 /
$$- \sin{\left(\frac{3 \pi}{a - 2} \right)} + \sin{\left(a + \frac{\pi}{2} \right)}$$ 
-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
$$- \frac{i \left(e^{\frac{3 i \pi}{2 - a}} - e^{- \frac{3 i \pi}{2 - a}}\right)}{2} + \frac{e^{i a}}{2} + \frac{e^{- i a}}{2}$$ 
exp(i*a)/2 + exp(-i*a)/2 - i*(-exp(-3*pi*i/(2 - a)) + exp(3*pi*i/(2 - a)))/2
    © Sr Examen