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ctg(y)=x la ecuación

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Solución numérica:

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Solución

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