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Simplificación de expresiones/ Descomposición en fracciones simples/ oo*sign(1/(cos(y)*sin(y)))

¿Cómo vas a descomponer esta oo*sign(1/(cos(y)*sin(y))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
       /      1      \
oo*sign|-------------|
       \cos(y)*sin(y)/
∞sign⁡(1sin⁡(y)cos⁡(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)/
∞sign⁡(1sin⁡(2y))\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  /                 /
∞isign⁡(1(eiy2+e−iy2)(eiy−e−iy))\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)  /
∞sign⁡(tan⁡2(y)+1tan⁡(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 //
∞sign⁡(1sin⁡(y)sin⁡(y+π2))\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 //
∞sign⁡(1cos⁡(y)cos⁡(y−π2))\infty \operatorname{sign}{\left(\frac{1}{\cos{\left(y \right)} \cos{\left(y - \frac{\pi}{2} \right)}} \right)} 
oo*sign(csc(2*y))
∞sign⁡(csc⁡(2y))\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//
∞sign⁡((cot⁡2(y2)+1)2(cot⁡2(y2)−1)cot⁡(y2))\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))
∞sign⁡(csc⁡(y)sec⁡(y))\infty \operatorname{sign}{\left(\csc{\left(y \right)} \sec{\left(y \right)} \right)} 
       /   1    \
oo*sign|--------|
       \sin(2*y)/
∞sign⁡(1sin⁡(2y))\infty \operatorname{sign}{\left(\frac{1}{\sin{\left(2 y \right)}} \right)} 
       /          /pi    \\
oo*sign|csc(y)*csc|-- - y||
       \          \2     //
∞sign⁡(csc⁡(y)csc⁡(−y+π2))\infty \operatorname{sign}{\left(\csc{\left(y \right)} \csc{\left(- y + \frac{\pi}{2} \right)} \right)} 
       /      1      \
oo*sign|-------------|
       |   /      pi\|
       |cos|2*y - --||
       \   \      2 //
∞sign⁡(1cos⁡(2y−π2))\infty \operatorname{sign}{\left(\frac{1}{\cos{\left(2 y - \frac{\pi}{2} \right)}} \right)} 
       /          /    pi\\
oo*sign|sec(y)*sec|y - --||
       \          \    2 //
∞sign⁡(sec⁡(y)sec⁡(y−π2))\infty \operatorname{sign}{\left(\sec{\left(y \right)} \sec{\left(y - \frac{\pi}{2} \right)} \right)} 
       /   /      pi\\
oo*sign|sec|2*y - --||
       \   \      2 //
∞sign⁡(sec⁡(2y−π2))\infty \operatorname{sign}{\left(\sec{\left(2 y - \frac{\pi}{2} \right)} \right)} 
       /       2   \
       |1 + cot (y)|
oo*sign|-----------|
       \   cot(y)  /
∞sign⁡(cot⁡2(y)+1cot⁡(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//
∞sign⁡((tan⁡2(y2)+1)2(1−tan⁡2(y2))tan⁡(y2))\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)))
Respuesta numérica [src] 
oo*sign(1/(cos(y)*sin(y)))
oo*sign(1/(cos(y)*sin(y)))
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