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BITSAT 2013

Exam: BITSAT
Year: 2013
Subject: Mathematics
Chapter: Inverse Trigonometric Functions

BITSAT 2013 · Mathematics · Inverse Trigonometric Functions

The value of [(1)/(2) ^ -1 ( ( ^ -1 63 8 ))] is -

The value of

\cos

\left[\frac{1}{2} \cos ^{-1}

\left(\cos \left(\sin ^{-1} \frac{\sqrt{63}}{8}\right)\right)\right]

is

-

Options

A $3 / 16$
B $3 / 8$
C $3 / 4$
D $3 / 2$

Correct answer

C. $3 / 4$

Step-by-step solution

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}

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