MHT CET · Maths · Inverse Trigonometric Functions
The value of \(\sin \left(2 \sin ^{-1} 0.8\right)\) is equal to
- A \(0.48\)
- B \(0.16\)
- C \(0.96\)
- D \(0.12\)
Answer & Solution
Correct Answer
(C) \(0.96\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \sin \left(2 \sin ^{-1} 0.8\right)=\sin \left[\sin ^{-1}\left\{2 \times 0.8 \sqrt{1-(0.8)^2}\right\}\right] \\ & =\sin \left\{\sin ^{-1}\{2 \times 0.8 \sqrt{1-0.64}\}\right\} \\ & =\sin \left\{\sin ^{-1}\{2 \times 0.8 \sqrt{0.36}\}\right\} \\ & =\sin \left\{\sin ^{-1}\{2 \times 0.8 \times 0.6\}\right\} \\ & =\sin \left(\sin ^{-1}(0.96)\right) \\ & =0.96\end{aligned}\)
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