Question

The value of $\cos \frac{1}{2}{\cos }^{-1}\cos {\sin }^{-1}\frac{\sqrt{63}}{8}$ is

• A. $\frac{3}{16}$
• B. $\frac{3}{8}$
• C. $\frac{3}{4}$
• D. $\frac{3}{2}$

Answer 1

Answer: (C)

The given trigonometric ratio
$=\cos \frac{1}{2}{\cos }^{-1}\cos {\cos }^{-1}\frac{1}{8}$
$=c\cos \frac{1}{2}{\cos }^{-1}\frac{1}{8}$
$=\sqrt{\frac{1+\cos {\cos }^{-1}\frac{1}{8}}{2}}=\frac{3}{4}$
Note: One may also proceed by writing the ratio as $\cos \frac{1}{2}{\sin }^{-1}\frac{\sqrt{63}}{8}$