tg(x)=-ctg((3*pi*n)/4) la ecuación
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Solución
Solución detallada
Tenemos la ecuación
$$\tan{\left(x \right)} = - \cot{\left(\frac{3 \pi n}{4} \right)}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{atan}{\left(- \cot{\left(\frac{3 \pi n}{4} \right)} \right)}$$
O
$$x = \pi n - \operatorname{atan}{\left(\cot{\left(\frac{3 \pi n}{4} \right)} \right)}$$
, donde n es cualquier número entero
/ / /3*pi*n\\\ / / /3*pi*n\\\
x1 = - re|atan|cot|------||| - I*im|atan|cot|------|||
\ \ \ 4 /// \ \ \ 4 ///
$$x_{1} = - \operatorname{re}{\left(\operatorname{atan}{\left(\cot{\left(\frac{3 \pi n}{4} \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\cot{\left(\frac{3 \pi n}{4} \right)} \right)}\right)}$$
x1 = -re(atan(cot(3*pi*n/4))) - i*im(atan(cot(3*pi*n/4)))
Suma y producto de raíces
[src]
/ / /3*pi*n\\\ / / /3*pi*n\\\
- re|atan|cot|------||| - I*im|atan|cot|------|||
\ \ \ 4 /// \ \ \ 4 ///
$$- \operatorname{re}{\left(\operatorname{atan}{\left(\cot{\left(\frac{3 \pi n}{4} \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\cot{\left(\frac{3 \pi n}{4} \right)} \right)}\right)}$$
/ / /3*pi*n\\\ / / /3*pi*n\\\
- re|atan|cot|------||| - I*im|atan|cot|------|||
\ \ \ 4 /// \ \ \ 4 ///
$$- \operatorname{re}{\left(\operatorname{atan}{\left(\cot{\left(\frac{3 \pi n}{4} \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\cot{\left(\frac{3 \pi n}{4} \right)} \right)}\right)}$$
/ / /3*pi*n\\\ / / /3*pi*n\\\
- re|atan|cot|------||| - I*im|atan|cot|------|||
\ \ \ 4 /// \ \ \ 4 ///
$$- \operatorname{re}{\left(\operatorname{atan}{\left(\cot{\left(\frac{3 \pi n}{4} \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\cot{\left(\frac{3 \pi n}{4} \right)} \right)}\right)}$$
/ / /3*pi*n\\\ / / /3*pi*n\\\
- re|atan|cot|------||| - I*im|atan|cot|------|||
\ \ \ 4 /// \ \ \ 4 ///
$$- \operatorname{re}{\left(\operatorname{atan}{\left(\cot{\left(\frac{3 \pi n}{4} \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\cot{\left(\frac{3 \pi n}{4} \right)} \right)}\right)}$$
-re(atan(cot(3*pi*n/4))) - i*im(atan(cot(3*pi*n/4)))