The value of $\sin \left(2 \sin ^{-1} 0.8\right)$ is equal to

The value of $\sin \left(2 \sin ^{-1} 0.8\right)$ is equal to
  1. $0.48$
  2. $0.16$
  3. $0.96$
  4. $0.12$

Solution

$\begin{aligned} & \sin \left(2 \sin ^{-1} 0.8\right)=\sin \left[\sin ^{-1}\left\{2 \times 0.8 \sqrt{1-(0.8)^2}\right\}\right] \\ & =\sin \left\{\sin ^{-1}\{2 \times 0.8 \sqrt{1-0.64}\}\right\} \\ & =\sin \left\{\sin ^{-1}\{2 \times 0.8 \sqrt{0.36}\}\right\} \\ & =\sin \left\{\sin ^{-1}\{2 \times 0.8 \times 0.6\}\right\} \\ & =\sin \left(\sin ^{-1}(0.96)\right) \\ & =0.96\end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 2)

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