уравнение: cos^2 2x = cos^2 4x

Question

уравнение:

cos^2 2x = cos^2 4x

Answer 1

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

cos(2x)=t

cos(4x)=2cos^2(2x)-1

t^2=(2t^2-1)^2

t^2=4t^4+1-4t^2

4t^4-5t^2+1=0

t^2=1  cos^2(2x)=1

x=Пk/2

t^2=1/4

t=+-1/2

cos2x=+-1/2

x=+-П/6+пk/2