Question

The value of $\cos \left[ \frac{1}{2} \cos^{-1}\left(\cos\left(\sin^{-1} \frac{\sqrt{63}}{8}\right)\right)\right]$ is -

• A. 44636
• B. 44628
• C. 44624
• D. 44622

Answer 1

Answer: (C)

44624

Answer 2

The given trigonometric ratio
$=\cos \left[\frac{1}{2}\left(\cos \left(\cos ^{-1} \frac{1}{8}\right)\right)\right]$
$=\cos \left(\frac{1}{2} \cos ^{-1} \frac{1}{8}\right)$
$=\sqrt{\frac{1+\cos \left(\cos ^{-1} \frac{1}{8}\right)}{2}}$
$=\frac{3}{4}$