\(\Leftrightarrow\cos2x-\sqrt{3}\cdot\sin2x=\sqrt{2}\)
\(\Leftrightarrow-\sqrt{3}\cdot\sin2x+\cos2x=\sqrt{2}\)
\(\Leftrightarrow\sqrt{3+1}\cdot\sin\left(2x+\alpha\right)=\sqrt{2}\)
\(\Leftrightarrow2\cdot\sin\left(2x+\alpha\right)=\sqrt{2}\)
\(\cos\alpha=-\dfrac{\sqrt{3}}{2};\sin a=\dfrac{1}{2}\)
=>\(\alpha=\dfrac{\Pi}{6}\)
\(\Leftrightarrow\sin\left(2x+\dfrac{\Pi}{6}\right)=\dfrac{\sqrt{2}}{2}=\sin\left(\dfrac{\Pi}{4}\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x+\dfrac{\Pi}{6}=\dfrac{\Pi}{4}+k2\Pi\\2x+\dfrac{\Pi}{6}=\dfrac{3}{4}\Pi+k2\Pi\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=\dfrac{\Pi}{12}+k2\Pi\\2x=\dfrac{7}{12}\Pi+k2\Pi\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{\Pi}{24}+k\Pi\\x=\dfrac{7}{24}\Pi+k\Pi\end{matrix}\right.\)
