\(\Leftrightarrow\left(\dfrac{1+cos6x}{2}\right)cos2x-\dfrac{1+cos2x}{2}=0\)
\(\Leftrightarrow cos2x+cos2x.cos6x-cos2x-1=0\)
\(\Leftrightarrow\dfrac{1}{2}cos8x+\dfrac{1}{2}cos4x-1=0\)
\(\Leftrightarrow cos8x+cos4x-2=0\)
\(\Leftrightarrow2cos^24x-1+cos4x-2=0\)
\(\Leftrightarrow2cos^24x+cos4x-3=0\)
\(\Rightarrow\left[{}\begin{matrix}cos4x=1\\cos4x=-\dfrac{3}{2}< -1\left(loại\right)\end{matrix}\right.\)
\(\Rightarrow4x=k2\pi\)
\(\Rightarrow x=\dfrac{k\pi}{2}\)
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