Question

$\sqrt{2+\sqrt{2+\sqrt{2+2\cos 8\theta }}}=2\cos \theta$

Answer 1

$\sqrt{2+\sqrt{2+\sqrt{2+2\cos 8\theta }}}$

$\Rightarrow \sqrt{2+\sqrt{2+\sqrt{2\times 2{\cos }^{2}4\theta }}}$

$\Rightarrow \sqrt{2+\sqrt{2+2\cos 4\theta }}$

$\Rightarrow \sqrt{2+2\cos 2\theta }$

$\Rightarrow 2\cos \theta$

$\theta =n\pi$ for all values of $n$