\(\Leftrightarrow\left[{}\begin{matrix}2cosx-\sqrt{2}=0\\tan2x-\sqrt{3}=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=\dfrac{\sqrt{2}}{2}\\tanx=\sqrt{3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{4}+k2\pi\\x=-\dfrac{\pi}{4}+k2\pi\\x=\dfrac{\pi}{3}+k\pi\end{matrix}\right.\)