Question

The value of $\sin (\frac{\pi }{3}-{\sin }^{-1}(-\frac{\sqrt{3}}{2}))$ is?

• A. $\sqrt{3}/2$
• B. $-\sqrt{3}/2$
• C. $1/2$
• D. $-1/2$

Answer 1

The correct option is A $\sqrt{3}/2$

$\because {\sin }^{-1}\left(\sin \theta \right)=\theta ,\theta \in [\frac{-\pi }{2},\frac{\pi }{2}]$
$\therefore {\sin }^{-1}(-\frac{\sqrt{3}}{2})=\frac{-\pi }{3}$
$\therefore \sin (\frac{\pi }{3}-{\sin }^{-1}\left(\frac{-\sqrt{3}}{2}\right))=\sin (\frac{\pi }{3}-\left(\frac{-\pi }{3}\right))$
$=\sin \left(\frac{2\pi }{3}\right)=\frac{\sqrt{3}}{2}$