\(2cos5x.cosx=2cos4x.cos2x+6cos^2x+2\)
\(\Leftrightarrow cos6x+cos4x=cos6x+cos2x+3\left(1+cos2x\right)+2\)
\(\Leftrightarrow cos4x=4cos2x+5\)
\(\Leftrightarrow2cos^22x-1=4cos2x+5\)
\(\Leftrightarrow cos^22x-2cos2x-3=0\)
\(\Rightarrow\left[{}\begin{matrix}cos2x=-1\\cos2x=3\left(loại\right)\end{matrix}\right.\)
\(\Rightarrow2x=\pi+k2\pi\)
\(\Rightarrow x=\dfrac{\pi}{2}+k\pi\)
\(\Rightarrow x=-\dfrac{\pi}{2};\dfrac{\pi}{2}\)
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