Solve y=sqrt{tan(x)}

$$y= \sqrt{ \tan ( x ) }$$

Solve for y (complex solution)

$$y=\sqrt{\tan(x)}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}$$

Solve for x

$$x=\pi +2\pi n_{24}+arcSin(y^{2}\left(y^{4}+1\right)^{-\frac{1}{2}})\text{, }n_{24}\in \mathrm{Z}\text{, }\exists n_{21}\in \mathrm{Z}\text{ : }\left(n_{21}<2n_{24}+2\text{ and }n_{21}>\left(arcSin(y^{2}\left(y^{4}+1\right)^{-\frac{1}{2}})+\frac{1}{2}\pi +2\pi n_{24}\right)\pi ^{-1}\right)\text{ and }\exists n_{6}\in \mathrm{Z}\text{ : }\left(not(\pi +2\pi n_{24}+arcSin(y^{2}\left(y^{4}+1\right)^{-\frac{1}{2}})<\pi n_{6})\text{ and }\pi +2\pi n_{24}+arcSin(y^{2}\left(y^{4}+1\right)^{-\frac{1}{2}})<\frac{1}{2}\pi +\pi n_{6}\right)$$

$$x=arcSin(y^{2}\left(y^{4}+1\right)^{-\frac{1}{2}})+2n_{43}\pi \text{, }n_{43}\in \mathrm{Z}\text{, }\exists n_{21}\in \mathrm{Z}\text{ : }\left(n_{21}<2n_{43}+1\text{ and }arcSin(y^{2}\left(y^{4}+1\right)^{-\frac{1}{2}})+2n_{43}\pi <\pi \left(n_{21}+\frac{1}{2}\right)\right)\text{ and }\exists n_{6}\in \mathrm{Z}\text{ : }\left(not(arcSin(y^{2}\left(y^{4}+1\right)^{-\frac{1}{2}})+2n_{43}\pi <\pi n_{6})\text{ and }arcSin(y^{2}\left(y^{4}+1\right)^{-\frac{1}{2}})+2n_{43}\pi <\frac{1}{2}\pi +\pi n_{6}\right)$$

Solve for y

$$y=\sqrt{\tan(x)}$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(x\geq \pi n_{1}\text{ and }x<\pi n_{1}+\frac{\pi }{2}\right)$$