Rozwiąż równanie trygonometryczne: 2 [latex] sin^{2} [/latex] x - 3cosx =3

[latex]2sin^2x-3cos x=3 \ 2(1-cos^2x)-3cos x-3=0 \ -2cos^2x-3cos x-1=0 \ 2cos^2x+3cos x+1=0 \ \ t:=cos x, quad tin[-1;1] \ \ 2t^2+3t+1=0\ Delta=9-8=1\ t=frac{-3-1}4=-1 lor t=frac{-3+1}4=-frac12 \ \ cos x=-1 lor cos x=-frac12 \ underline{x=pi+2kpi lor x=frac23pi+2kpi lor x=-frac23+2kpi, quad kinmathbb{Z}}[/latex] Pzdr

[latex]2sin^{2}x - 3cosx = 3\\2(1-cos^{2}x) - 3cosx = 3\\2-2cos^{2}x - 3cosx = 3\\-2cos^{2}x - 3cosx -1 = 0\\2cos^{2}x +3cosx+1 = 0\\Delta = 9-8 = 1, sqrt{Delta} = 1\\cosx =frac{-3-1}{4} = -1 vee cosx = frac{-3+1}{4} = -frac{1}{2}[/latex] [latex]x = pi +2k pi vee x = frac{2}{3} pi +2k pi vee x = frac{4}{3} pi+2k pi [/latex]