Question

Prove that: $2\cos \theta =\sqrt{2+\sqrt{(2+2\cos 4\theta )}}$

Answer 1

LHS $=\sqrt{2+\sqrt{(2+2\cos 4\theta )}}=\sqrt{2+\sqrt{2(1+\cos 4\theta )}}=\sqrt{2+2\cos 2\theta }=\sqrt{2(1+\cos 2\theta )}=2\cos \theta$