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The value of \( \sin \left(2 \sin ^{-1} 0.8\right) \) is equal to
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The correct answer is:
\( 0.96 \)
Given that, $\sin \left(2 \sin ^{-1} 0.8\right)$
Let $\sin ^{-1} 0.8=\theta \Rightarrow \sin \theta=0.8$
So, $\cos \theta=\sqrt{1-\sin ^{2} \theta}=0.6$
We know that, $\sin 2 \theta=2 \sin \theta \cos \theta$
$=2 \times 0.8 \times 0.6=1.6 \times 0.6$
$=0.96$
Let $\sin ^{-1} 0.8=\theta \Rightarrow \sin \theta=0.8$
So, $\cos \theta=\sqrt{1-\sin ^{2} \theta}=0.6$
We know that, $\sin 2 \theta=2 \sin \theta \cos \theta$
$=2 \times 0.8 \times 0.6=1.6 \times 0.6$
$=0.96$
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