Find the value of [2 ^ -1 (0.6) ] - Vidyadip

Question

Find the value of $\sin \left[2 \sin ^{-1}(0.6)\right]$

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Answer

We know that $2 \sin ^{-1} x=\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)$, if$
\begin{array}{l}
\frac{-1}{\sqrt{2}} \leq x \leq \frac{1}{\sqrt{2}} \\
\therefore \quad 2 \sin ^{-1}(0.6)=\sin ^{-1}(2 \times 0.6 \times \sqrt{1-0.36}) \\
=\sin ^{-1}(0.96) \\
\Rightarrow \quad \sin \left(2 \sin ^{-1}(0.6)\right)=\sin \left(\sin ^{-1}(0.96)\right) \\
=0.96 \text { }
\end{array}
$

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