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cos(x)^2*sin(y)*cos(y)+sin(x)*cos(x)*cos(y)+sin(x)*cos(x)*sin(y)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   2                                                                   
cos (x)*sin(y)*cos(y) + sin(x)*cos(x)*cos(y) + sin(x)*cos(x)*sin(y) = 0
$$\sin{\left(x \right)} \cos{\left(x \right)} \sin{\left(y \right)} + \left(\sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(y \right)} + \sin{\left(y \right)} \cos^{2}{\left(x \right)} \cos{\left(y \right)}\right) = 0$$
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      2  
$$x_{1} = - \frac{\pi}{2}$$
     pi
x2 = --
     2 
$$x_{2} = \frac{\pi}{2}$$
           /    /       1   \\         /    /       1   \\
           |    | 1 + ------||         |    | 1 + ------||
           |    |        /y\||         |    |        /y\||
           |    |     tan|-|||         |    |     tan|-|||
           |    |        \2/||         |    |        \2/||
x3 = - 2*re|atan|-----------|| - 2*I*im|atan|-----------||
           |    |        /y\||         |    |        /y\||
           |    |-1 + tan|-|||         |    |-1 + tan|-|||
           \    \        \2///         \    \        \2///
$$x_{3} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1 + \frac{1}{\tan{\left(\frac{y}{2} \right)}}}{\tan{\left(\frac{y}{2} \right)} - 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1 + \frac{1}{\tan{\left(\frac{y}{2} \right)}}}{\tan{\left(\frac{y}{2} \right)} - 1} \right)}\right)}$$
         /    //        /y\\    /y\\\         /    //        /y\\    /y\\\
         |    ||-1 + tan|-||*tan|-|||         |    ||-1 + tan|-||*tan|-|||
         |    |\        \2//    \2/||         |    |\        \2//    \2/||
x4 = 2*re|atan|--------------------|| + 2*I*im|atan|--------------------||
         |    |            /y\     ||         |    |            /y\     ||
         |    |     1 + tan|-|     ||         |    |     1 + tan|-|     ||
         \    \            \2/     //         \    \            \2/     //
$$x_{4} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\left(\tan{\left(\frac{y}{2} \right)} - 1\right) \tan{\left(\frac{y}{2} \right)}}{\tan{\left(\frac{y}{2} \right)} + 1} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\left(\tan{\left(\frac{y}{2} \right)} - 1\right) \tan{\left(\frac{y}{2} \right)}}{\tan{\left(\frac{y}{2} \right)} + 1} \right)}\right)}$$
x4 = 2*re(atan((tan(y/2) - 1)*tan(y/2)/(tan(y/2) + 1))) + 2*i*im(atan((tan(y/2) - 1)*tan(y/2)/(tan(y/2) + 1)))