Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sin((\pi)/(2)+a)+cos(\pi+a)+ctg(2\pi-a)+tg((3\pi)/(2)-a)
¿Cómo vas a descomponer esta sin((\pi)/(2)+a)+cos(\pi+a)+ctg(2\pi-a)+tg((3\pi)/(2)-a) expresión en fracciones?
Solución
Ha introducido
[src]
//3 \ \
||--| |
/pi \ /2 \ |\pi/ |
sin|-- + a| + cos(pi + a) + cot|-- - a| + tan|---- - a|
\2 / \pi / \ 2 /
$$\left(\left(\sin{\left(a + \frac{\pi}{2} \right)} + \cos{\left(a + \pi \right)}\right) + \cot{\left(- a + \frac{2}{\pi} \right)}\right) + \tan{\left(- a + \frac{3 \frac{1}{\pi}}{2} \right)}$$
sin(pi/2 + a) + cos(pi + a) + cot(2/pi - a) + tan((3/pi)/2 - a)
Simplificación general
[src]
/ 2 \ / 3 \
- cot|a - --| - tan|a - ----|
\ pi/ \ 2*pi/
$$- \tan{\left(a - \frac{3}{2 \pi} \right)} - \cot{\left(a - \frac{2}{\pi} \right)}$$
-cot(a - 2/pi) - tan(a - 3/(2*pi))
Respuesta numérica
[src]
cos(pi + a) + cot(2/pi - a) + sin(pi/2 + a) + tan((3/pi)/2 - a)
cos(pi + a) + cot(2/pi - a) + sin(pi/2 + a) + tan((3/pi)/2 - a)
Denominador racional
[src]
/ 2 \ / 3 \ / pi\
-cos(a) - cot|a - --| - tan|a - ----| + sin|a + --|
\ pi/ \ 2*pi/ \ 2 /
$$\sin{\left(a + \frac{\pi}{2} \right)} - \cos{\left(a \right)} - \tan{\left(a - \frac{3}{2 \pi} \right)} - \cot{\left(a - \frac{2}{\pi} \right)}$$
-cos(a) - cot(a - 2/pi) - tan(a - 3/(2*pi)) + sin(a + pi/2)
Unión de expresiones racionales
[src]
/2 - pi*a\ /pi + 2*a\ /3 - 2*pi*a\
-cos(a) + cot|--------| + sin|--------| + tan|----------|
\ pi / \ 2 / \ 2*pi /
$$\sin{\left(\frac{2 a + \pi}{2} \right)} - \cos{\left(a \right)} + \tan{\left(\frac{- 2 \pi a + 3}{2 \pi} \right)} + \cot{\left(\frac{- \pi a + 2}{\pi} \right)}$$
-cos(a) + cot((2 - pi*a)/pi) + sin((pi + 2*a)/2) + tan((3 - 2*pi*a)/(2*pi))
Potencias
[src]
/ / pi\ / pi\\ / / 3 \ / 3 \\
| I*|-a - --| I*|a + --|| | I*|-a + ----| I*|a - ----||
I*(pi + a) I*(-pi - a) | \ 2 / \ 2 /| | \ 2*pi/ \ 2*pi/|
e e / 2 \ I*\- e + e / I*\- e + e /
----------- + ------------ - cot|a - --| - -------------------------------- + ------------------------------------
2 2 \ pi/ 2 / 3 \ / 3 \
I*|a - ----| I*|-a + ----|
\ 2*pi/ \ 2*pi/
e + e
$$\frac{i \left(- e^{i \left(- a + \frac{3}{2 \pi}\right)} + e^{i \left(a - \frac{3}{2 \pi}\right)}\right)}{e^{i \left(- a + \frac{3}{2 \pi}\right)} + e^{i \left(a - \frac{3}{2 \pi}\right)}} - \frac{i \left(- e^{i \left(- a - \frac{\pi}{2}\right)} + e^{i \left(a + \frac{\pi}{2}\right)}\right)}{2} + \frac{e^{i \left(- a - \pi\right)}}{2} + \frac{e^{i \left(a + \pi\right)}}{2} - \cot{\left(a - \frac{2}{\pi} \right)}$$
/ 2 \ / 3 \
- cot|a - --| - tan|a - ----|
\ pi/ \ 2*pi/
$$- \tan{\left(a - \frac{3}{2 \pi} \right)} - \cot{\left(a - \frac{2}{\pi} \right)}$$
-cot(a - 2/pi) - tan(a - 3/(2*pi))
Compilar la expresión
[src]
//3 \ \
||--| |
/2 \ /pi \ |\pi/ |
cos(pi + a) + cot|-- - a| + sin|-- + a| + tan|---- - a|
\pi / \2 / \ 2 /
$$\sin{\left(a + \frac{\pi}{2} \right)} + \cos{\left(a + \pi \right)} + \tan{\left(- a + \frac{3 \frac{1}{\pi}}{2} \right)} + \cot{\left(- a + \frac{2}{\pi} \right)}$$
cos(pi + a) + cot(2/pi - a) + sin(pi/2 + a) + tan((3/pi)/2 - a)
Denominador común
[src]
/ 2 \ / 3 \
- cot|a - --| - tan|a - ----| + cos(a) + cos(pi + a)
\ pi/ \ 2*pi/
$$\cos{\left(a \right)} + \cos{\left(a + \pi \right)} - \tan{\left(a - \frac{3}{2 \pi} \right)} - \cot{\left(a - \frac{2}{\pi} \right)}$$
-cot(a - 2/pi) - tan(a - 3/(2*pi)) + cos(a) + cos(pi + a)
Combinatoria
[src]
/ 2 \ / 3 \
- cot|a - --| - tan|a - ----|
\ pi/ \ 2*pi/
$$- \tan{\left(a - \frac{3}{2 \pi} \right)} - \cot{\left(a - \frac{2}{\pi} \right)}$$
-cot(a - 2/pi) - tan(a - 3/(2*pi))