Решите уравнение

cos^4 (2x) - cos^2 (4x) = 0

(1+cos4x) ²/4-cos²4x=0

1+2cos4x+cos²4x-4cos²4x=0

3cos²4x-2cos4x-1=0

cos4x=a

3a²-2a-1=0

D=4+12=16

a1 = (2-4) / 6=-1/3⇒cos4x=-1/3⇒4x = + - (π-arccos1/3) + 2πn⇒

x=+-1/4 (π-arccos1/3) + πn/2

a2 = (2+4) / 6=1⇒cos4x=1⇒4x=2πn⇒x=πn/2