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sin(y)*cos(x)=cos(y)*sin(x) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
sin(y)*cos(x) = cos(y)*sin(x)
sin⁡(y)cos⁡(x)=sin⁡(x)cos⁡(y)\sin{\left(y \right)} \cos{\left(x \right)} = \sin{\left(x \right)} \cos{\left(y \right)}
Simplificar
Solución detallada
Tenemos la ecuación
sin⁡(y)cos⁡(x)=sin⁡(x)cos⁡(y)\sin{\left(y \right)} \cos{\left(x \right)} = \sin{\left(x \right)} \cos{\left(y \right)}
cambiamos:
−sin⁡(x)cos⁡(y)cos⁡(x)=−sin⁡(y)- \frac{\sin{\left(x \right)} \cos{\left(y \right)}}{\cos{\left(x \right)}} = - \sin{\left(y \right)}
o
−cos⁡(y)tan⁡(x)=−sin⁡(y)- \cos{\left(y \right)} \tan{\left(x \right)} = - \sin{\left(y \right)}
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en -cos(y)

La ecuación se convierte en
tan⁡(x)=−sin⁡(y)cos⁡(y)\tan{\left(x \right)} = - \frac{\sin{\left(y \right)}}{\cos{\left(y \right)}}
Esta ecuación se reorganiza en
x=πn+atan⁡(−sin⁡(y)cos⁡(y))x = \pi n + \operatorname{atan}{\left(- \frac{\sin{\left(y \right)}}{\cos{\left(y \right)}} \right)}
O
x=πn−atan⁡(sin⁡(y)cos⁡(y))x = \pi n - \operatorname{atan}{\left(\frac{\sin{\left(y \right)}}{\cos{\left(y \right)}} \right)}
, donde n es cualquier número entero
Gráfica
Suma y producto de raíces [src] 
suma
      /    /  1   \\         /    /  1   \\       /    /   /y\\\         /    /   /y\\\
- 2*re|atan|------|| - 2*I*im|atan|------|| + 2*re|atan|tan|-||| + 2*I*im|atan|tan|-|||
      |    |   /y\||         |    |   /y\||       \    \   \2///         \    \   \2///
      |    |tan|-|||         |    |tan|-|||                                            
      \    \   \2///         \    \   \2///
(−2re⁡(atan⁡(1tan⁡(y2)))−2iim⁡(atan⁡(1tan⁡(y2))))+(2re⁡(atan⁡(tan⁡(y2)))+2iim⁡(atan⁡(tan⁡(y2))))\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\tan{\left(\frac{y}{2} \right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\tan{\left(\frac{y}{2} \right)} \right)}\right)}\right) 
=
      /    /  1   \\       /    /   /y\\\         /    /  1   \\         /    /   /y\\\
- 2*re|atan|------|| + 2*re|atan|tan|-||| - 2*I*im|atan|------|| + 2*I*im|atan|tan|-|||
      |    |   /y\||       \    \   \2///         |    |   /y\||         \    \   \2///
      |    |tan|-|||                              |    |tan|-|||                       
      \    \   \2///                              \    \   \2///
−2re⁡(atan⁡(1tan⁡(y2)))+2re⁡(atan⁡(tan⁡(y2)))−2iim⁡(atan⁡(1tan⁡(y2)))+2iim⁡(atan⁡(tan⁡(y2)))- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\tan{\left(\frac{y}{2} \right)} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\tan{\left(\frac{y}{2} \right)} \right)}\right)} 
producto
/      /    /  1   \\         /    /  1   \\\ /    /    /   /y\\\         /    /   /y\\\\
|- 2*re|atan|------|| - 2*I*im|atan|------|||*|2*re|atan|tan|-||| + 2*I*im|atan|tan|-||||
|      |    |   /y\||         |    |   /y\||| \    \    \   \2///         \    \   \2////
|      |    |tan|-|||         |    |tan|-||||                                            
\      \    \   \2///         \    \   \2////
(−2re⁡(atan⁡(1tan⁡(y2)))−2iim⁡(atan⁡(1tan⁡(y2))))(2re⁡(atan⁡(tan⁡(y2)))+2iim⁡(atan⁡(tan⁡(y2))))\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\tan{\left(\frac{y}{2} \right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\tan{\left(\frac{y}{2} \right)} \right)}\right)}\right) 
=
   /    /    /  1   \\     /    /  1   \\\ /    /    /   /y\\\     /    /   /y\\\\
-4*|I*im|atan|------|| + re|atan|------|||*|I*im|atan|tan|-||| + re|atan|tan|-||||
   |    |    |   /y\||     |    |   /y\||| \    \    \   \2///     \    \   \2////
   |    |    |tan|-|||     |    |tan|-||||                                        
   \    \    \   \2///     \    \   \2////
−4(re⁡(atan⁡(1tan⁡(y2)))+iim⁡(atan⁡(1tan⁡(y2))))(re⁡(atan⁡(tan⁡(y2)))+iim⁡(atan⁡(tan⁡(y2))))- 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\tan{\left(\frac{y}{2} \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\tan{\left(\frac{y}{2} \right)} \right)}\right)}\right) 
-4*(i*im(atan(1/tan(y/2))) + re(atan(1/tan(y/2))))*(i*im(atan(tan(y/2))) + re(atan(tan(y/2))))
Respuesta rápida [src] 
           /    /  1   \\         /    /  1   \\
x1 = - 2*re|atan|------|| - 2*I*im|atan|------||
           |    |   /y\||         |    |   /y\||
           |    |tan|-|||         |    |tan|-|||
           \    \   \2///         \    \   \2///
x1=−2re⁡(atan⁡(1tan⁡(y2)))−2iim⁡(atan⁡(1tan⁡(y2)))x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)} 
         /    /   /y\\\         /    /   /y\\\
x2 = 2*re|atan|tan|-||| + 2*I*im|atan|tan|-|||
         \    \   \2///         \    \   \2///
x2=2re⁡(atan⁡(tan⁡(y2)))+2iim⁡(atan⁡(tan⁡(y2)))x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\tan{\left(\frac{y}{2} \right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\tan{\left(\frac{y}{2} \right)} \right)}\right)} 
x2 = 2*re(atan(tan(y/2))) + 2*i*im(atan(tan(y/2)))
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