2cos(квадрат)2x + cos2x + cos6x = 1

Question

2cos(квадрат)2x + cos2x + cos6x = 1

Answer 1

2cos²2x-1+cos2x+cos6x=0
cos2(2x)+cos2x+cos6x=0
cos4x+cos2x+cos6x=0
cos4x+2*cos(6x+2x)/2*cos(6x-2x)/2=0
cos4x+2cos4x*cos2x=0
cos4x(1+2cos2x)=0
cos4x=0
4x=π*n/2
x=π*n/8
1+2cos2x=0
2cos2x=-1
cos2x=-1/2
2x=2π/3+2πn
x=π/3+πn
2x=4π/3+2πn
x=2π/3+πn