Sqrt( cos^2 x - sin^2 x ) (tg2x-1 )=0

[latex]\sqrt{cos^2x-sin^2x}\cdot (tg2x-1)=0\\\\\sqrt{cos2x}\cdot (tg2x-1)=0\\\\a)\quad cos2x=0\; \; \to \; \; 2x=\frac{\pi}{2}+\pi n,\; n\in Z\\\\x=\frac{\pi}{4}+\frac{\pi n}{2}\; ,\; n\in Z\\\\b)\quad tg2x=1\; \; \to \; \; 2x=\frac{\pi}{4}+\pi k\; ,\; k\in Z\\\\x=\frac{\pi}{8}+\frac{\pi k}{2}\; ,\; k\in Z[/latex]