\(\Leftrightarrow\left(sin^2x+cos^2x\right)^2-2sin^2x.cos^2x=2cos2x\)
\(\Leftrightarrow1-\frac{1}{2}sin^22x=2cos2x\)
\(\Leftrightarrow2-\left(1-cos^22x\right)=4cos2x\)
\(\Leftrightarrow cos^22x-4cos2x+1=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos2x=2+\sqrt{3}>1\left(l\right)\\cos2x=2-\sqrt{3}\end{matrix}\right.\)
\(\Leftrightarrow x=\pm\frac{1}{2}arccos\left(2-\sqrt{3}\right)+k\pi\)
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