cos(y)=x-3 la ecuación
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Solución
Solución detallada
Tenemos la ecuación
$$\cos{\left(y \right)} = x - 3$$
cambiamos
$$- x + \cos{\left(y \right)} + 2 = 0$$
$$- x + \cos{\left(y \right)} + 2 = 0$$
Sustituimos
$$w = \cos{\left(y \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w - x = -2$$
Move the summands with the other variables
del miembro izquierdo al derecho, obtenemos:
$$w = x + -2$$
Obtenemos la respuesta: w = -2 + x
hacemos cambio inverso
$$\cos{\left(y \right)} = w$$
sustituimos w:
Suma y producto de raíces
[src]
3 + cos(re(y))*cosh(im(y)) - I*sin(re(y))*sinh(im(y))
$$- i \sin{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} + \cos{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} + 3$$
3 + cos(re(y))*cosh(im(y)) - I*sin(re(y))*sinh(im(y))
$$- i \sin{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} + \cos{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} + 3$$
3 + cos(re(y))*cosh(im(y)) - I*sin(re(y))*sinh(im(y))
$$- i \sin{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} + \cos{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} + 3$$
3 + cos(re(y))*cosh(im(y)) - I*sin(re(y))*sinh(im(y))
$$- i \sin{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} + \cos{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} + 3$$
3 + cos(re(y))*cosh(im(y)) - i*sin(re(y))*sinh(im(y))
x1 = 3 + cos(re(y))*cosh(im(y)) - I*sin(re(y))*sinh(im(y))
$$x_{1} = - i \sin{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} + \cos{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} + 3$$
x1 = -i*sin(re(y))*sinh(im(y)) + cos(re(y))*cosh(im(y)) + 3