\(cos2x-\sqrt{3}sin2x=cosx+\sqrt{3}sinx\)
\(\Leftrightarrow\dfrac{1}{2}cos2x-\dfrac{\sqrt{3}}{2}sin2x=\dfrac{1}{2}cosx+\dfrac{\sqrt{3}}{2}sinx\)
\(\Leftrightarrow cos\left(2x+\dfrac{\pi}{3}\right)=cos\left(x-\dfrac{\pi}{3}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+\dfrac{\pi}{3}=x-\dfrac{\pi}{3}+k2\pi\\2x+\dfrac{\pi}{3}=\dfrac{\pi}{3}-x+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{2\pi}{3}+k2\pi\\x=\dfrac{k2\pi}{3}\end{matrix}\right.\)
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