Question

Evaluate $\sin [\frac{\pi }{3}-{\sin }^{-1}(-\frac{1}{2}\left)\right]$

• A. $-1$
• B. $0$
• C. $1$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$1$

$\sin \{\frac{\pi }{3}-{\sin }^{-1}(-\frac{1}{2}\left)\right\}$

Let $y={\sin }^{-1}(-\frac{1}{2})$

$\sin y=(-\frac{1}{2})$

$y=-\frac{\pi }{6}$

$\sin \left\{\frac{\pi }{3}\right(-\frac{\pi }{6}\left)\right\}$

$=\sin (\frac{\pi }{3}+\frac{\pi }{6})$

$=\sin (9\times \frac{\pi }{18})$

$=\sin \left(\frac{\pi }{2}\right)$

$=1$