KCET · Maths · Differentiation
The value of \( \sin \left(2 \sin ^{-1} 0.8\right) \) is equal to
- A \( \sin 1.2^{\circ} \)
- B \( 0.96 \)
- C \( 0.48 \)
- D \( \sin 1.6^{\circ} \)
Answer & Solution
Correct Answer
(B) \( 0.96 \)
Step-by-step Solution
Detailed explanation
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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