\(\dfrac{sin2x}{\sqrt{3}}=cos^4\dfrac{x}{2}-sin^4\dfrac{x}{2}\)
\(\Leftrightarrow\dfrac{sin2x}{\sqrt{3}}=\left(cos^2\dfrac{x}{2}-sin^2\dfrac{x}{2}\right)\left(cos^2\dfrac{x}{2}+sin^2\dfrac{x}{2}\right)\)
\(\Leftrightarrow sin2x=\sqrt{3}\left(cos^2\dfrac{x}{2}-sin^2\dfrac{x}{2}\right)\)
\(\Leftrightarrow2sinx.cosx=\sqrt{3}cosx\)
\(\Leftrightarrow\left(2sinx-\sqrt{3}\right).cosx=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=\dfrac{\sqrt{3}}{2}\\cosx=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{3}+k2\pi\\x=\dfrac{2\pi}{3}+k2\pi\\x=\dfrac{\pi}{2}+k\pi\end{matrix}\right.\)
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