Question

The value of $cos\left(\frac{1}{2}co{s}^{-1}\frac{1}{8}\right)$ is

• A. $\frac{3}{4}$
• B. $-\frac{3}{4}$
• C. $\frac{1}{16}$
• D. $\frac{1}{4}$

Answer 1

The correct option is A $\frac{3}{4}$

We know, $cos\left(\frac{\theta }{2}\right)$ $=\sqrt{\frac{1+cos\theta }{2}}$
Substituting $\theta =co{s}^{-1}\left(\frac{1}{8}\right)$
We get, $\sqrt{\frac{1+\frac{1}{8}}{2}}$
$=\sqrt{\frac{9}{16}}$
$=\frac{3}{4}$