Question

$\sqrt{2+\sqrt{2+2cos4\theta }}$ is equal to

• A. $cos\theta$
• B. $2cos\theta$
• C. $cos2\theta$
• D. $2cos3\theta$

Answer 1

The correct option is B $2cos\theta$

Using $cos2x=2{cos}^{2}x-1$
We get
$\sqrt{2+\sqrt{2+2cos4\theta }}=\sqrt{2+\sqrt{2+2(2{cos}^{2}2\theta -1)}}$
$=\sqrt{2+\sqrt{2+4{cos}^{2}2\theta -2}}=\sqrt{2+2cos2\theta }$
$=\sqrt{2+2(2{cos}^2\theta -1)}=\sqrt{4{cos}^2\theta }=2cos\theta$