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] 3pi/8 + pi n [/latex]