căn2*cos2x + sinx - cosx = 0

$\sqrt2\cos2x+\sin x-\cos x=0$

$\to \sqrt2(\cos^2x-\sin^2x)-(\cos x-\sin x)=0$

$\to (\cos x-\sin x).(\sqrt2(\cos x+\sin x)-1)=0$

$\to \sqrt2\sin\left(x-\dfrac{\pi}{4}\right).\Bigg( \sqrt2\sin\left(x+\dfrac{\pi}{4}\right)-1\Bigg)=0$ 

$\to \left[ \begin{array}{l}\sin\left(x-\dfrac{\pi}{4}\right)=0 \\\sin\left(x+\dfrac{\pi}{4}\right)=\dfrac{1}{\sqrt2}\end{array} \right.$

$\to \left[ \begin{array}{l}x=\dfrac{\pi}{4}+k\pi \\x=k2\pi \\ x=\dfrac{\pi}{2}+k2\pi \end{array} \right.$