Solve 2cos^2(2x)=1

Question

I divided both sides by 2 and got this

cos^2(2x)=1/2

But then I didn't know what to do after that... The part that has me stumped is that it's a cos^2(2x) not just a cos^2x. Any advice on what I should try next?

Answer 1

well, if cos^2(2x) = 1/2,
cos(2x) = ±1/√2, so

2x = π/4 or 3π/4 or 5π/4 or 7π/4
That means that x is π/8,3π/8,...