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sin(x)×(sin(x)+sin(y))+cos(x)×(cos(x)+cos(y))=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
sin(x)*(sin(x) + sin(y)) + cos(x)*(cos(x) + cos(y)) = 0
$$\left(\sin{\left(x \right)} + \sin{\left(y \right)}\right) \sin{\left(x \right)} + \left(\cos{\left(x \right)} + \cos{\left(y \right)}\right) \cos{\left(x \right)} = 0$$
Gráfica
Respuesta rápida [src]
           /    /  1   \\         /    /  1   \\
x1 = - 2*re|atan|------|| - 2*I*im|atan|------||
           |    |   /y\||         |    |   /y\||
           |    |tan|-|||         |    |tan|-|||
           \    \   \2///         \    \   \2///
$$x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)}$$
x1 = -2*re(atan(1/tan(y/2))) - 2*i*im(atan(1/tan(y/2)))
Suma y producto de raíces [src]
suma
      /    /  1   \\         /    /  1   \\
- 2*re|atan|------|| - 2*I*im|atan|------||
      |    |   /y\||         |    |   /y\||
      |    |tan|-|||         |    |tan|-|||
      \    \   \2///         \    \   \2///
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)}$$
=
      /    /  1   \\         /    /  1   \\
- 2*re|atan|------|| - 2*I*im|atan|------||
      |    |   /y\||         |    |   /y\||
      |    |tan|-|||         |    |tan|-|||
      \    \   \2///         \    \   \2///
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)}$$
producto
      /    /  1   \\         /    /  1   \\
- 2*re|atan|------|| - 2*I*im|atan|------||
      |    |   /y\||         |    |   /y\||
      |    |tan|-|||         |    |tan|-|||
      \    \   \2///         \    \   \2///
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)}$$
=
      /    /  1   \\         /    /  1   \\
- 2*re|atan|------|| - 2*I*im|atan|------||
      |    |   /y\||         |    |   /y\||
      |    |tan|-|||         |    |tan|-|||
      \    \   \2///         \    \   \2///
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{y}{2} \right)}} \right)}\right)}$$
-2*re(atan(1/tan(y/2))) - 2*i*im(atan(1/tan(y/2)))