\(\Leftrightarrow cos2x.cosx+2cos2x+sin2x.cosx-sinx=0\)
\(\Leftrightarrow cos2x.cosx+2cos2x+2sinx.cos^2x-sinx=0\)
\(\Leftrightarrow cos2x.cosx+2cos2x+sinx\left(2cos^2x-1\right)=0\)
\(\Leftrightarrow cos2x.cosx+2cos2x+sinx.cos2x=0\)
\(\Leftrightarrow cos2x\left(cosx+2+sinx\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos2x=0\\\sqrt{2}sin\left(x+\frac{\pi}{4}\right)=-2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=\frac{\pi}{2}+k\pi\\sin\left(x+\frac{\pi}{4}\right)=-\sqrt{2}< -1\left(vn\right)\end{matrix}\right.\)
\(\Rightarrow x=\frac{\pi}{4}+\frac{k\pi}{2}\)
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