\(\Leftrightarrow sinx.cos^2x-sin^3x+\sqrt{3}cos^3x-\sqrt{3}sin^2x.cosx=0\)
\(\Leftrightarrow sinx\left(cos^2x-sin^2x\right)+\sqrt{3}cosx\left(cos^2x-sin^2x\right)=0\)
\(\Leftrightarrow\left(cos^2x-sin^2x\right)\left(sinx+\sqrt{3}cosx\right)=0\)
\(\Leftrightarrow cos2x.\left(\frac{1}{2}sinx+\frac{\sqrt{3}}{2}cosx\right)=0\)
\(\Leftrightarrow cos2x.sin\left(x+\frac{\pi}{3}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos2x=0\\sin\left(x+\frac{\pi}{3}\right)=0\end{matrix}\right.\) \(\Leftrightarrow...\)
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