\(\Leftrightarrow2cos2x.cos\left(\dfrac{\pi}{4}\right)+4sinx=2+\sqrt{2}-\sqrt{2}sinx\)
\(\Leftrightarrow\sqrt{2}cos2x+\left(4+\sqrt{2}\right)sinx-2-\sqrt{2}=0\)
\(\Leftrightarrow\sqrt{2}-2\sqrt{2}sin^2x+\left(4+\sqrt{2}\right)sinx-2-\sqrt{2}=0\)
\(\Leftrightarrow-2\sqrt{2}sin^2x+\left(4+\sqrt{2}\right)sinx-2=0\)
\(\Rightarrow\left[{}\begin{matrix}sinx=\sqrt{2}\left(loại\right)\\sinx=\dfrac{1}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{6}+k2\pi\\x=\dfrac{5\pi}{6}+k2\pi\end{matrix}\right.\)
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