Prove the trig identity

Question

cos(4x)=2-sec^2(2x)/sec^2(2x)

Answer 1

cos(4x) = 2-sec^2(2x)/sec^2(2x)
= 2 cos^2(2x) - 1
= cos^2 (2x) - sin^2(2x)

Now.. do you rememember the double angle formula for cos (2y) ?
Let y = 2x