Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
cos((7pi/24)+pi/8)/(√6*sin(pi/10+(3pi)/20))
¿Cómo vas a descomponer esta cos((7pi/24)+pi/8)/(√6*sin(pi/10+(3pi)/20)) expresión en fracciones?
Solución
Ha introducido
[src]
/7*pi pi\
cos|---- + --|
\ 24 8 /
--------------------
___ /pi 3*pi\
\/ 6 *sin|-- + ----|
\10 20 /
$$\frac{\cos{\left(\frac{\pi}{8} + \frac{7 \pi}{24} \right)}}{\sqrt{6} \sin{\left(\frac{\pi}{10} + \frac{3 \pi}{20} \right)}}$$
cos((7*pi)/24 + pi/8)/((sqrt(6)*sin(pi/10 + (3*pi)/20)))
Simplificación general
[src]
___ ___
\/ 6 \/ 2
- ----- + -----
12 4
$$- \frac{\sqrt{6}}{12} + \frac{\sqrt{2}}{4}$$
-sqrt(6)/12 + sqrt(2)/4
Denominador racional
[src]
___ /7*pi pi\
\/ 6 *cos|---- + --|
\ 24 8 /
--------------------
/3*pi pi\
6*sin|---- + --|
\ 20 10/
$$\frac{\sqrt{6} \cos{\left(\frac{\pi}{8} + \frac{7 \pi}{24} \right)}}{6 \sin{\left(\frac{\pi}{10} + \frac{3 \pi}{20} \right)}}$$
sqrt(6)*cos(7*pi/24 + pi/8)/(6*sin(3*pi/20 + pi/10))
Unión de expresiones racionales
[src]
/ ___ ___\
___ | \/ 2 \/ 6 |
\/ 3 *|- ----- + -----|
\ 4 4 /
-----------------------
3
$$\frac{\sqrt{3} \left(- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\right)}{3}$$
sqrt(3)*(-sqrt(2)/4 + sqrt(6)/4)/3
Denominador común
[src]
___ ___
\/ 6 \/ 2
- ----- + -----
12 4
$$- \frac{\sqrt{6}}{12} + \frac{\sqrt{2}}{4}$$
-sqrt(6)/12 + sqrt(2)/4
Combinatoria
[src]
___ / ___ ___\
-\/ 3 *\\/ 2 - \/ 6 /
-----------------------
12
$$- \frac{\sqrt{3} \left(- \sqrt{6} + \sqrt{2}\right)}{12}$$
-sqrt(3)*(sqrt(2) - sqrt(6))/12
Potencias
[src]
/ ___ ___\
___ | \/ 2 \/ 6 |
\/ 3 *|- ----- + -----|
\ 4 4 /
-----------------------
3
$$\frac{\sqrt{3} \left(- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\right)}{3}$$
/ ___ ___\
___ | \/ 2 \/ 6 |
\/ 3 *|- ----- + -----|
\ 12 12 /
$$\sqrt{3} \left(- \frac{\sqrt{2}}{12} + \frac{\sqrt{6}}{12}\right)$$
/ -5*pi*I 5*pi*I\
| ------- ------|
| 12 12 |
___ |e e |
I*\/ 6 *|-------- + -------|
\ 2 2 /
----------------------------
/ -pi*I pi*I\
| ------ ----|
| 4 4 |
3*\- e + e /
$$\frac{\sqrt{6} i \left(\frac{e^{- \frac{5 i \pi}{12}}}{2} + \frac{e^{\frac{5 i \pi}{12}}}{2}\right)}{3 \left(- e^{- \frac{i \pi}{4}} + e^{\frac{i \pi}{4}}\right)}$$
i*sqrt(6)*(exp(-5*pi*i/12)/2 + exp(5*pi*i/12)/2)/(3*(-exp(-pi*i/4) + exp(pi*i/4)))
Parte trigonométrica
[src]
/ 2\
| / ___ ___\ |
| | \/ 2 \/ 6 | |
/ 2\ | | - ----- + -----| |
___ | / ___\ | | | 1 4 4 | |
\/ 6 *\1 + \1 + \/ 2 / /*|-1 + |------------- + ---------------| |
| | ___ ___ ___ ___ | |
| |\/ 2 \/ 6 \/ 2 \/ 6 | |
| |----- + ----- ----- + ----- | |
\ \ 4 4 4 4 / /
------------------------------------------------------------------
/ 2\
| / ___ ___\ |
| | \/ 2 \/ 6 | |
| | - ----- + -----| |
| | 1 4 4 | | / ___\
6*|1 + |------------- + ---------------| |*\2 + 2*\/ 2 /
| | ___ ___ ___ ___ | |
| |\/ 2 \/ 6 \/ 2 \/ 6 | |
| |----- + ----- ----- + ----- | |
\ \ 4 4 4 4 / /
$$\frac{\sqrt{6} \left(-1 + \left(\frac{- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} + \frac{1}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}}\right)^{2}\right) \left(1 + \left(1 + \sqrt{2}\right)^{2}\right)}{6 \left(1 + \left(\frac{- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} + \frac{1}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}}\right)^{2}\right) \left(2 + 2 \sqrt{2}\right)}$$
/ ___ ___\
___ | \/ 2 \/ 6 | /-pi \
\/ 6 *|- ----- + -----|*sec|----|
\ 4 4 / \ 4 /
---------------------------------
6
$$\frac{\sqrt{6} \left(- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\right) \sec{\left(- \frac{\pi}{4} \right)}}{6}$$
/ ___ ___\
___ | \/ 2 \/ 6 |
\/ 3 *|- ----- + -----|
\ 4 4 /
-----------------------
3
$$\frac{\sqrt{3} \left(- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\right)}{3}$$
___ /11*pi\
\/ 3 *sin|-----|
\ 12 /
----------------
3
$$\frac{\sqrt{3} \sin{\left(\frac{11 \pi}{12} \right)}}{3}$$
/ ___ ___\
___ | \/ 2 \/ 6 |
\/ 6 *|- ----- + -----|
\ 4 4 /
-----------------------
/-pi \
6*cos|----|
\ 4 /
$$\frac{\sqrt{6} \left(- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\right)}{6 \cos{\left(- \frac{\pi}{4} \right)}}$$
___ / ___ ___\
\/ 3 *\\/ 6 - \/ 2 /
---------------------
12
$$\frac{\sqrt{3} \left(- \sqrt{2} + \sqrt{6}\right)}{12}$$
/ 2\
| / ___ ___\ |
| | \/ 2 \/ 6 | |
/ 2\ | | - ----- + -----| |
___ | / ___\ | | | 1 4 4 | |
\/ 6 *\1 + \-1 + \/ 2 / /*|1 - |------------- - ---------------| |
| | ___ ___ ___ ___ | |
| |\/ 2 \/ 6 \/ 2 \/ 6 | |
| |----- + ----- ----- + ----- | |
\ \ 4 4 4 4 / /
------------------------------------------------------------------
/ 2\
| / ___ ___\ |
| | \/ 2 \/ 6 | |
| | - ----- + -----| |
| | 1 4 4 | | / ___\
6*|1 + |------------- - ---------------| |*\-2 + 2*\/ 2 /
| | ___ ___ ___ ___ | |
| |\/ 2 \/ 6 \/ 2 \/ 6 | |
| |----- + ----- ----- + ----- | |
\ \ 4 4 4 4 / /
$$\frac{\sqrt{6} \left(1 - \left(- \frac{- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} + \frac{1}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}}\right)^{2}\right) \left(\left(-1 + \sqrt{2}\right)^{2} + 1\right)}{6 \left(-2 + 2 \sqrt{2}\right) \left(\left(- \frac{- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} + \frac{1}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}}\right)^{2} + 1\right)}$$
sqrt(6)*(1 + (-1 + sqrt(2))^2)*(1 - (1/(sqrt(2)/4 + sqrt(6)/4) - (-sqrt(2)/4 + sqrt(6)/4)/(sqrt(2)/4 + sqrt(6)/4))^2)/(6*(1 + (1/(sqrt(2)/4 + sqrt(6)/4) - (-sqrt(2)/4 + sqrt(6)/4)/(sqrt(2)/4 + sqrt(6)/4))^2)*(-2 + 2*sqrt(2)))