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