ĐKXĐ: \(x\ne\dfrac{\pi}{4}+k\pi\)
\(\Rightarrow cos^2x+2sinx.cosx+3sin^2x+3\sqrt{2}sinx=sin2x-1\)
\(\Leftrightarrow1+2sin^2x+3\sqrt{2}sinx=-1\)
\(\Leftrightarrow2sin^2x+3\sqrt{2}sinx+2=0\)
\(\Rightarrow\left[{}\begin{matrix}sinx=-\sqrt{2}\left(loại\right)\\sinx=-\dfrac{\sqrt{2}}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{4}+k2\pi\\x=\dfrac{5\pi}{4}+k2\pi\end{matrix}\right.\)
\(\Rightarrow x=-\dfrac{\pi}{4}+k2\pi\)
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