Question

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

• 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 that $\sqrt{\frac{1+cos2A}{2}}=cosA$

Therefore

$cos\left(\frac{1}{2}co{s}^{-1}\left(\frac{1}{8}\right)\right)=\sqrt{\frac{1+cos\left(co{s}^{-1}\left(\frac{1}{8}\right)\right)}{2}}$

$=\sqrt{\frac{1+\frac{1}{8}}{2}}$

$=\sqrt{\frac{9}{16}}$

$=\frac{3}{4}$