Question

Simplest form of $\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2+2\cos 4x}}}}$ is

• A. $\sec \frac{x}{2}$
• B. $\sec x$
• C. $cosecx$
• D. $1$

Answer 1

Answer: (A)

$\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2+2\cos 4x}}}}$

$=\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2\cdot 2{\cos }^{2}2x}}}}$

$=\frac{2}{\sqrt{2+\sqrt{2+2\cos 2x}}}$

$=\frac{2}{\sqrt{2+2\cos x}}$

$=\frac{2}{2\cos \frac{x}{2}}=\sec \frac{x}{2}$