\(\Leftrightarrow cos8x+cos2x+sinx=cos8x\)
\(\Leftrightarrow cos2x=-sinx\)
\(\Leftrightarrow cos2x=cos\left(x+\frac{\pi}{2}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=x+\frac{\pi}{2}+k2\pi\\2x=-x-\frac{\pi}{2}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow...\)