[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 extless 0; o ; ne ; podxodit\\(cosx)_2=frac{-1+3}{4}=frac{1}{2} geq 0; ,; x=pm frac{pi}{3}+2pi n; ,; nin Z[/latex][latex]b); ; cosx extless 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} extless 0; ,; x=pm frac{2pi}{3}+2pi m,; min Z\\(cosx)_4=1 extgreater 0; o ; ne; podxodit\\Otvet:; x=pm frac{pi}{3}+2pi n,; nin Z; ;; x=pm frac{2pi}{3}+2pi m,; min Z\\oo[/latex]