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The value of
$\cos \left[\frac{1}{2} \cos ^{-1}\left(\cos \left(\sin ^{-1} \frac{\sqrt{63}}{8}\right)\right)\right]$ is $-$
Options:
$\cos \left[\frac{1}{2} \cos ^{-1}\left(\cos \left(\sin ^{-1} \frac{\sqrt{63}}{8}\right)\right)\right]$ is $-$
Solution:
1744 Upvotes
Verified Answer
The correct answer is:
$3 / 4$
The given trigonometric ratio
$$
\begin{array}{l}
=\cos \left[\frac{1}{2}\left(\cos \left(\cos ^{-1} \frac{1}{8}\right)\right)\right] \\
=\cos \left(\frac{1}{2} \cos ^{-1} \frac{1}{8}\right) \\
=\sqrt{\frac{1+\cos \left(\cos ^{-1} \frac{1}{8}\right)}{2}}=\frac{3}{4}
\end{array}
$$
$$
\begin{array}{l}
=\cos \left[\frac{1}{2}\left(\cos \left(\cos ^{-1} \frac{1}{8}\right)\right)\right] \\
=\cos \left(\frac{1}{2} \cos ^{-1} \frac{1}{8}\right) \\
=\sqrt{\frac{1+\cos \left(\cos ^{-1} \frac{1}{8}\right)}{2}}=\frac{3}{4}
\end{array}
$$
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