Sr Examen
¿Cómo vas a descomponer esta oo*sign(1/(cos(y)*sin(y))) expresión en fracciones?
Solución
Ha introducido
[src]
/ 1 \
oo*sign|-------------|
\cos(y)*sin(y)/
$$\infty \operatorname{sign}{\left(\frac{1}{\sin{\left(y \right)} \cos{\left(y \right)}} \right)}$$
oo*sign(1/(cos(y)*sin(y)))
Simplificación general
[src]
/ 1 \
oo*sign|--------|
\sin(2*y)/
$$\infty \operatorname{sign}{\left(\frac{1}{\sin{\left(2 y \right)}} \right)}$$
oo*sign(1/sin(2*y))
Potencias
[src]
/ 1 \
oo*I*sign|-------------------------------|
|/ I*y -I*y\ |
||e e | / -I*y I*y\|
||---- + -----|*\- e + e /|
\\ 2 2 / /
$$\infty i \operatorname{sign}{\left(\frac{1}{\left(\frac{e^{i y}}{2} + \frac{e^{- i y}}{2}\right) \left(e^{i y} - e^{- i y}\right)} \right)}$$
oo*i*sign(1/((exp(i*y)/2 + exp(-i*y)/2)*(-exp(-i*y) + exp(i*y))))
Parte trigonométrica
[src]
/ 2 \
|1 + tan (y)|
oo*sign|-----------|
\ tan(y) /
$$\infty \operatorname{sign}{\left(\frac{\tan^{2}{\left(y \right)} + 1}{\tan{\left(y \right)}} \right)}$$
/ 1 \
oo*sign|------------------|
| / pi\|
|sin(y)*sin|y + --||
\ \ 2 //
$$\infty \operatorname{sign}{\left(\frac{1}{\sin{\left(y \right)} \sin{\left(y + \frac{\pi}{2} \right)}} \right)}$$
/ 1 \
oo*sign|------------------|
| / pi\|
|cos(y)*cos|y - --||
\ \ 2 //
$$\infty \operatorname{sign}{\left(\frac{1}{\cos{\left(y \right)} \cos{\left(y - \frac{\pi}{2} \right)}} \right)}$$
oo*sign(csc(2*y))
$$\infty \operatorname{sign}{\left(\csc{\left(2 y \right)} \right)}$$
/ 2 \
| / 2/y\\ |
| |1 + cot |-|| |
| \ \2// |
oo*sign|---------------------|
|/ 2/y\\ /y\|
||-1 + cot |-||*cot|-||
\\ \2// \2//
$$\infty \operatorname{sign}{\left(\frac{\left(\cot^{2}{\left(\frac{y}{2} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{y}{2} \right)} - 1\right) \cot{\left(\frac{y}{2} \right)}} \right)}$$
oo*sign(csc(y)*sec(y))
$$\infty \operatorname{sign}{\left(\csc{\left(y \right)} \sec{\left(y \right)} \right)}$$
/ 1 \
oo*sign|--------|
\sin(2*y)/
$$\infty \operatorname{sign}{\left(\frac{1}{\sin{\left(2 y \right)}} \right)}$$
/ /pi \\
oo*sign|csc(y)*csc|-- - y||
\ \2 //
$$\infty \operatorname{sign}{\left(\csc{\left(y \right)} \csc{\left(- y + \frac{\pi}{2} \right)} \right)}$$
/ 1 \
oo*sign|-------------|
| / pi\|
|cos|2*y - --||
\ \ 2 //
$$\infty \operatorname{sign}{\left(\frac{1}{\cos{\left(2 y - \frac{\pi}{2} \right)}} \right)}$$
/ / pi\\
oo*sign|sec(y)*sec|y - --||
\ \ 2 //
$$\infty \operatorname{sign}{\left(\sec{\left(y \right)} \sec{\left(y - \frac{\pi}{2} \right)} \right)}$$
/ / pi\\
oo*sign|sec|2*y - --||
\ \ 2 //
$$\infty \operatorname{sign}{\left(\sec{\left(2 y - \frac{\pi}{2} \right)} \right)}$$
/ 2 \
|1 + cot (y)|
oo*sign|-----------|
\ cot(y) /
$$\infty \operatorname{sign}{\left(\frac{\cot^{2}{\left(y \right)} + 1}{\cot{\left(y \right)}} \right)}$$
/ 2 \
| / 2/y\\ |
| |1 + tan |-|| |
| \ \2// |
oo*sign|--------------------|
|/ 2/y\\ /y\|
||1 - tan |-||*tan|-||
\\ \2// \2//
$$\infty \operatorname{sign}{\left(\frac{\left(\tan^{2}{\left(\frac{y}{2} \right)} + 1\right)^{2}}{\left(1 - \tan^{2}{\left(\frac{y}{2} \right)}\right) \tan{\left(\frac{y}{2} \right)}} \right)}$$
oo*sign((1 + tan(y/2)^2)^2/((1 - tan(y/2)^2)*tan(y/2)))