\[\sqrt{2 + \sqrt{2 + 2\cos 4\theta}} =] | MATH - FUNDAMENTAL TRIGONOMETRICAL | SolveeIt | Solveeit

Today, August 18

Question

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

A

$\cos\theta$

B

$\sin\theta$

C

$2\cos\theta$

D

$2\sin\theta$

Answer

$2\cos\theta$

Explanation

Solution

$\sqrt{2 + \sqrt{2 + 2\cos 4\theta}}$ = $\sqrt{2 + \sqrt{2.2\cos^{2}2\theta}}$

$= \sqrt{2 + 2\cos 2\theta} = \sqrt{4\cos^{2}\theta} = 2\cos\theta$ .