\(\Leftrightarrow2\sqrt{2}cos2x+sin2x\left(cosx.cos\left(\frac{3\pi}{4}\right)-sinx.sin\left(\frac{3\pi}{4}\right)\right)-2\sqrt{2}\left(sinx+cosx\right)=0\)
\(\Leftrightarrow2\left(cos^2x-sin^2x\right)-sinx.cosx\left(cosx+sinx\right)-2\left(sinx+cosx\right)=0\)
\(\Leftrightarrow\left(sinx+cosx\right)\left(2cosx-2sinx-sinx.cosx-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx+cosx=0\Rightarrow...\\2\left(cosx-sinx\right)-sinx.cosx-2=0\left(1\right)\end{matrix}\right.\)
Xét (1)
Đặt \(cosx-sinx=t\Rightarrow sinx.cosx=\frac{1-t^2}{2}\) (với \(\left|t\right|\le\sqrt{2}\))
\(\Rightarrow2t-\frac{1-t^2}{2}-2=0\Leftrightarrow t^2+4t-5=0\Rightarrow\left[{}\begin{matrix}t=1\\t=-5\left(vn\right)\end{matrix}\right.\)
\(\Rightarrow cosx-sinx=1\Leftrightarrow\sqrt{2}cos\left(x+\frac{\pi}{4}\right)=1\Leftrightarrow cos\left(x+\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2}\Leftrightarrow...\)
