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MHT CET · Maths · Inverse Trigonometric Functions

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

  1. A \(0.48\)
  2. B \(0.16\)
  3. C \(0.96\)
  4. D \(0.12\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(0.96\)

Step-by-step Solution

Detailed explanation

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