Question

Prove that:

$\sqrt{2+\sqrt{2+2cos4\theta }}=2cos\theta$

Answer 1

LHS,

$\sqrt{2+\sqrt{2+2cos4\theta }}=\sqrt{2+\sqrt{2(1+cos4\theta )}}=\sqrt{2+\sqrt{2.2co{s}^{2}2\theta }}=\sqrt{2+\sqrt{2cos2\theta }}=\sqrt{2\sqrt{(1+cos2\theta )}}=\sqrt{2.2co{s}^2\theta }$