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. $cosec\, x$
• D. $1$

Answer 1

Answer: (A)

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

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

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

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

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