a) [latex]\1-cos2x=tgx \ \1-(cos^2x-sin^2x)- frac{sinx}{cosx} =0/*cosx \ \(1-cos^2x+sin^2x)*cosx-sinx=0 \ \cosx*2sin^2x-sinx=0 \ \sinx(2sinx*cosx-1)=0 \ \sinx(sin2x-1)=0 \ \sinx=0 vee sin2x=1 \ \x=kpi vee 2x= frac{pi}{2} +2kpi , kin C \ \x=kpi vee x= frac{pi}{4} +kpi.[/latex] b) [latex]\sin^2 2x - cos^2 2x = cos2x \ \1-cos^22x-cos^22x-cos2x=0/*(-1) \ \2cos^22x+cos2x-1=0, cos2x=t \ \2t^2+t-1=0 \ \Delta=1+4*2=9 \ \t_1= frac{-1-3}{4} =-1, t_2= frac{-1+3}{4} = frac{1}{2} \ \cos2x=-1 vee cos2x= frac{1}{2} \ \2x=pi+2kpi vee 2x= frac{pi}{3} +2kpi vee x=- frac{pi}{3} +2kpi \ \x= frac{pi}{2} +kpi vee x= frac{pi}{6} +kpi vee x=- frac{pi}{6} +kpi, kin C[/latex] c) [latex]\2cos^2 2x - 3sin 2x = 0 \ \2(1-sin^22x)-3sin2x=0, sin2x=tin extless -1,1 extgreater \ \-2t^2-3t+2=0 \ \Delta=9+4*2*2=25 \ \t_1= frac{3+5}{-4} =-2 otin D, t_2= frac{3-5}{-4} = frac{1}{2} \ \sin2x= frac{1}{2} \ \2x= frac{pi}{6} +2kpi vee x=(pi- frac{pi}{6} )+2kpi, kin C \ \x= frac{pi}{12} +kpi vee x= frac{5}{12} pi+kpi[/latex]
Zadanie w załączniku. Liczę na naj.
