Question

$(\frac{\pi }{3}-si{n}^{-1}(-\frac{1}{2}\left)\right)$ is equal

Answer 1

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

$=-{\text{sin}}^{-1}\left(\sin \frac{\pi }{6}\right)$

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

$\frac{\pi }{3}-{\text{sin}}^{-1}(-\frac{1}{2})=\frac{\pi }{3}-(-\frac{\pi }{6})$

$=\frac{\pi }{3}+\frac{\pi }{6}$

$=\frac{2\pi +\pi }{6}$

$=\frac{3\pi }{6}$

$=\frac{\pi }{2}$