$cos2x=cos(x-\frac{\pi}{4}) \\
\Leftrightarrow \left[\begin{matrix}
2x=x-\frac{\pi}{4}+k2\pi & \\ \\
2x=-x+\frac{\pi}{4}+k2\pi &
\end{matrix}\right. \\ \\
\Leftrightarrow \left[\begin{matrix}
x=-\frac{\pi}{4}+k2\pi & \\ \\
x=\frac{\pi}{12}+\frac{k2\pi}{3} &
\end{matrix}\right. k \in \mathbb{Z}$
