Solucionar y=tan(x+pi/6)

$$y= \tan ( x+ \frac{ \pi }{ 6 } )$$

Resolver para y (solución compleja)

$$y=-\frac{ie^{\frac{6ix+\pi i}{3}}-i}{e^{\frac{6ix+\pi i}{3}}+1}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{3}$$

Resolver para x

$$x=2n_{4}\pi +\frac{5}{6}\pi +arcSin(y\left(y^{2}+1\right)^{-\frac{1}{2}})\text{, }n_{4}\in \mathrm{Z}\text{, }\exists n_{43}\in \mathrm{Z}\text{ : }\left(n_{4}>-\frac{1}{4}+\left(-\frac{1}{2}\right)\pi ^{-1}arcSin(y\left(y^{2}+1\right)^{-\frac{1}{2}})+\frac{1}{2}n_{43}\text{ and }n_{4}<\frac{1}{4}+\left(-\frac{1}{2}\right)\pi ^{-1}arcSin(y\left(y^{2}+1\right)^{-\frac{1}{2}})+\frac{1}{2}n_{43}\right)$$

$$x=\left(-\frac{1}{6}\right)\pi +arcSin(y\left(y^{2}+1\right)^{-\frac{1}{2}})+2\pi n_{23}\text{, }n_{23}\in \mathrm{Z}\text{, }\exists n_{43}\in \mathrm{Z}\text{ : }\left(n_{43}<\pi ^{-1}arcSin(y\left(y^{2}+1\right)^{-\frac{1}{2}})-\frac{1}{2}+2n_{23}\text{ and }n_{43}>\pi ^{-1}arcSin(y\left(y^{2}+1\right)^{-\frac{1}{2}})-\frac{3}{2}+2n_{23}\right)$$

Resolver para y

$$y=\frac{\sqrt{3}\sin(x)+\cos(x)}{\sqrt{3}\cos(x)-\sin(x)}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{3}$$