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

Question

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

Answer 1

(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