Question

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

• A. $-\frac{31}{32}$
• B. $\frac{3}{4}$
• C. $-\frac{\sqrt{7}}{4}$
• D. $-\frac{3}{7}$

Answer 1

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

Let $\theta =co{s}^{-1}\left(\frac{1}{8}\right)$
$cos\theta =\frac{1}{8}\therefore cos(\frac{1}{2}.co{s}^{-1}\left(\frac{1}{8}\right))=cos\left(\frac{\theta }{2}\right)=\sqrt{\frac{cos\theta +1}{2}}=\sqrt{\frac{\frac{1}{8}+1}{2}}=\sqrt{\frac{9}{8.2}}=+\frac{3}{4}or-\frac{3}{4}$