[latex]2sin^2x-|cosx|-1=0[/latex]

[latex]2sin^2x-|cosx|-1=0\\\\a)\; \; cosx \geq 0\; ,\; |cosx|=cosx\; ,\; \; 2sin^2x-cosx-1=0\\\\2(1-cos^2x)-cosx-1=0\\\\2cos^2x+cosx-1=0\\\\D=9\; ,\; (cosx)_1=\frac{-1-3}{4}=-1\ \textless \ 0\; \to \; ne \; podxodit\\\\(cosx)_2=\frac{-1+3}{4}=\frac{1}{2} \geq 0\; ,\; x=\pm \frac{\pi}{3}+2\pi n\; ,\; n\in Z[/latex] [latex]b)\; \; cosx\ \textless \ 0\; ,\; |cosx|=-cosx\; ,\; 2sin^2x+cosx-1=0\\\\2(1-cos^2x)+cosx-1=0\\\\2cos^2x-cosx-1=0\\\\(cosx)_3=-\frac{1}{2}\ \textless \ 0\; ,\; x=\pm \frac{2\pi}{3}+2\pi m,\; m\in Z\\\\(cosx)_4=1\ \textgreater \ 0\; \to \; ne\; podxodit\\\\Otvet:\; x=\pm \frac{\pi}{3}+2\pi n,\; n\in Z\; ;\; \ x=\pm \frac{2\pi}{3}+2\pi m,\; m\in Z\\\\oo[/latex]