(2*sinx+√2)/(2*cosx-√2)=0

[latex] \frac{2sinx+\sqrt2}{2cosx-\sqrt2} =0\; \; \to \; \; \left \{ {{2sinx+\sqrt2=0} \atop {2cosx-\sqrt2\ne 0}} \right. \; ,\; \left \{ {{sinx=-\frac{\sqrt2}{2}} \atop {cosx\ne \frac{\sqrt2}{2}}} \right. \\\\\\ \left \{ {{x=(-1)^{n+1}\frac{\pi}{4}+\pi n\; ,\; n\in Z} \atop {x=\pm \frac{\pi}{4}+2\pi k\; ,\; k \in Z}} \right. \; \; \to \; \; x=-\frac{3\pi }{4}+2\pi n\; ,\; n\in Z\\[/latex]