Тригонометрия. cos4x + 2cos^2x=1

Преобразуем cos4x = 2[latex] cos^{2}2x [/latex] 2[latex] cos^{2}2x -1+2 cos^{2}2x = 1 [/latex] [latex] 4cos^{2}2x = 2 [/latex] [latex] cos^{2}2x = 1/2 [/latex] cos2x = [latex] \sqrt{2} /2[/latex]              cos2x = -[latex] \sqrt{2}/2 [/latex] 2x = +-[latex] \pi /4 + 2 \pi n[/latex]              2x = +-[latex]3 \pi /4 + 2 \pi n[/latex] x = +-[latex] \pi /8 + \pi n[/latex]                    x= +-[latex] 3\pi/8 + \pi n [/latex]