Atrisiniet y=(cos2x)^2

$$y = ( \cos 2 x ) ^ { 2 }$$

Atrast x

$$\left\{\begin{matrix}x=\frac{\arccos(\sqrt{y})+2\pi n_{1}}{2}\text{, }n_{1}\in \mathrm{Z}\text{; }x=\frac{-\arccos(\sqrt{y})+2\pi n_{2}}{2}\text{, }n_{2}\in \mathrm{Z}\text{, }&y\leq 1\text{ and }y\geq 0\text{ and }\sqrt{y}\leq 1\\x=\frac{-\arccos(\sqrt{y})+2\pi n_{3}+\pi }{2}\text{, }n_{3}\in \mathrm{Z}\text{; }x=\frac{\arccos(\sqrt{y})+2\pi n_{4}-\pi }{2}\text{, }n_{4}\in \mathrm{Z}\text{, }&y\leq 1\text{ and }y\geq 0\text{ and }-\sqrt{y}\geq -1\end{matrix}\right,$$

Atrast y

$$y=\left(\cos(2x)\right)^{2}$$