Cos4x-cos2x=1. Указать корни ** отрезке [П\2;2П]

Question

Cos4x-cos2x=1. Указать корни на отрезке [П\2;2П]

Answer 1

2cos^22x-cos2x-2=0

 

cos2x=(1+-3)/4

cos2x=1                2x=2Пl   x=Пl   (П ; 2П)

cos2x=-1/2            2х=П+-П/3+2Пk

                                            x=П/2+-П/6+Пk

                                            x= 2П/3

                                             x=5П/3