y=tan2x-ஐ தீர்க்கவும்

$$y = \tan 2 x$$

x-க்காகத் தீர்க்கவும்

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

$$x=\frac{1}{2}arcSin(y\left(y^{2}+1\right)^{-\frac{1}{2}})+\pi n_{23}\text{, }n_{23}\in \mathrm{Z}\text{, }\left(\left(\nexists n_{1}\in \mathrm{Z}\text{ : }\frac{1}{2}arcSin(y\left(y^{2}+1\right)^{-\frac{1}{2}})+\pi n_{23}=\frac{1}{4}\pi +\frac{1}{2}\pi n_{1}\text{ and }\exists n_{43}\in \mathrm{Z}\text{ : }\left(n_{43}<\pi ^{-1}arcSin(y\left(y^{2}+1\right)^{-\frac{1}{2}})-\frac{1}{2}+2n_{23}\text{ and }n_{43}>\pi ^{-1}arcSin(y\left(y^{2}+1\right)^{-\frac{1}{2}})-\frac{3}{2}+2n_{23}\right)\right)\text{ and }\exists n_{43}\in \mathrm{Z}\text{ : }\left(n_{43}<\pi ^{-1}arcSin(y\left(y^{2}+1\right)^{-\frac{1}{2}})-\frac{1}{2}+2n_{23}\text{ and }n_{43}>\pi ^{-1}arcSin(y\left(y^{2}+1\right)^{-\frac{1}{2}})-\frac{3}{2}+2n_{23}\right)\right)\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\frac{1}{2}arcSin(y\left(y^{2}+1\right)^{-\frac{1}{2}})+\pi n_{23}=\frac{1}{4}\pi +\frac{1}{2}\pi n_{1}$$

y-க்காகத் தீர்க்கவும்

$$y=\tan(2x)$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{2}+\frac{\pi }{4}$$