Q. Simplest form of $\frac{2}{\sqrt{2 + \sqrt{2 + \sqrt{2 + 2\cos{4x}}}}}$ is
A) $\sec\frac{x}{2}$
B) $\sec x$
C) $cosec\ x$
D) 1
Explanation
(a)
$\frac{2}{\sqrt{2 + \sqrt{2 + \sqrt{2 + 2\cos{4x}}}}}$
$= \frac{2}{\sqrt{2 + \sqrt{2 + \sqrt{2.2\cos^{2}{2x}}}}}$
$= \frac{2}{\sqrt{2 + \sqrt{2 + 2\cos{2x}}}}$
$= \frac{2}{\sqrt{2 + 2\cos x}} = \frac{2}{2\cos\frac{x}{2}} = \sec\frac{x}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.