\(\Leftrightarrow sinx+\sqrt{3}cosx=2sin3x+2sinx\)
\(\Leftrightarrow\sqrt{3}cosx-sinx=2sin3x\)
\(\Leftrightarrow\dfrac{\sqrt{3}}{2}cosx-\dfrac{1}{2}sinx=sin3x\)
\(\Leftrightarrow cos\left(x+\dfrac{\pi}{6}\right)=cos\left(\dfrac{\pi}{2}-3x\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{\pi}{6}=\dfrac{\pi}{2}-3x+k2\pi\\x+\dfrac{\pi}{6}=3x-\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{12}+\dfrac{k\pi}{2}\\x=\dfrac{\pi}{3}+k\pi\end{matrix}\right.\)
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