Question

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

• A. sin $1.2^{\circ}$
• B. $0.96$
• C. $0.48$
• D. sin $1.6^{\circ}$

Answer 1

Answer: (B)

Let $E =\sin \left(2 \sin ^{-1} 0.8\right)$
Put $\sin ^{-1} 0.8=\theta$
$\Rightarrow \sin \theta=0.8$
$\therefore \cos \theta =\sqrt{1-\sin ^{2} \theta}$
$=\sqrt{1-0.64}=\sqrt{0.36}=0.6$
$\therefore E =\sin (2 \theta)=2 \sin \theta \cos \theta$
$=2 \times 0.8 \times 0.6=0.96$