2sinx(1+cos2x)=1+2cosx-sin2x.
\(\Leftrightarrow2sinx\left(1+2cos^2x-1\right)=1+2cosx-sin2x\)
\(\Leftrightarrow4sinxcos^2x=1+2cosx-sin2x\)
\(\Leftrightarrow2cosx\left(sin2x-1\right)=1-sin2x\)
\(\Leftrightarrow\left(2cosx-1\right)\left(sin2x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2cosx-1=0\\sin2x-1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\pm\dfrac{\pi}{3}+2k\pi\\x=\dfrac{\pi}{4}+k\pi\end{matrix}\right.\)
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