Question

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

• A. $\sin 2\theta$
• B. $2\sin \theta$
• C. $2\cos \theta$
• D. $2\cos \frac{\theta }{2}$

Answer 1

Answer: (C)

$1+\cos \theta =2{\cos }^2\left(\frac{\theta }{2}\right)$
$\sqrt{2+\sqrt{2+\sqrt{2+2\cos 8\theta }}}=2\cos \theta$