Resolver x+cos2a+sin2a/1-cos2a+sin2a=operatorname{ctg}a

$$\frac { x + \cos 2 a + \sin 2 a } { 1 - \cos 2 a + \sin 2 a } = \operatorname { ctg } a$$

Ebatzi: a (complex solution)

$$a\in \mathrm{C}$$

$$x=1\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\left(a=\pi n_{1}+\frac{3\pi }{4}\text{ or }a=\pi n_{1}\right)$$

Ebatzi: x (complex solution)

$$\left\{\begin{matrix}x=1\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\left(a=\pi n_{1}+\frac{3\pi }{4}\text{ or }a=\pi n_{1}\right)\\x\in \mathrm{C}\text{, }&\left(-2-2i\right)\sin(2a)e^{ia}+\left(2-2i\right)\sin(2a)e^{-ia}=0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }a=\pi n_{2}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\left(a=\pi n_{1}+\frac{3\pi }{4}\text{ or }a=\pi n_{1}\right)\end{matrix}\right.$$

Ebatzi: a

$$a\notin \pi n_{1}+\frac{3\pi }{4},\pi n_{1}$$

$$\forall n_{1}\in \mathrm{Z}$$

$$x=1$$

Ebatzi: x

$$x=1$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\left(a=\pi n_{1}+\frac{3\pi }{4}\text{ or }a=\pi n_{1}\right)$$