\(cos4x+2sin^2x=sin\left(2x+\dfrac{\pi}{2}\right)\)
\(\Leftrightarrow2cos^22x-1+1-cos2x=cos2x\)
\(\Leftrightarrow2cos^22x-2cos2x=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos2x=0\\cos2x=1\end{matrix}\right.\)
\(\Leftrightarrow...\)
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