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  4. The value of cos (1/2) cos -1 cos sin -1 (√63/8) is

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

NTA AbhyasNTA Abhyas 2022

Solution:

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 $\cos \frac{1}{2} \sin ^{-1} \frac{\sqrt{63}}{8}$