Sin^2x+2cos^2x-5cosx-7=0

[latex]sin ^{2} x+2cos ^{2} x-5cosx-7=0[/latex] [latex]1-cos ^{2} x+2cos ^{2} x-5cosx-7=0[/latex] [latex]cos ^{2} x-5cosx-6=0[/latex] [latex]cosx=t[/latex] [latex] t^{2} -5t-6=0[/latex] D = (-5)² - 4·1·(-6) = 25 + 24 = 49 [latex] \sqrt{D} =7[/latex] [latex] t_{1} = \frac{5+7}{2} = \frac{12}{2} =6[/latex] [latex] t_{2} = \frac{5-7}{2} = \frac{-2}{2}=-1 [/latex] [latex] \left \{ {{cosx=6} \atop {cosx=-1}} \right. [/latex] Ø [latex]x= \pi +2 \pi k,[/latex] k∈Z