Question

Write the value of sin \[\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\}\]

Answer 1

We have
\[\sin\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\} = \sin\left\{ \frac{\pi}{3} - \left( - \frac{\pi}{6} \right) \right\}\]
\[ = \sin\left\{ \frac{\pi}{3} + \frac{\pi}{6} \right\}\]
\[ = \sin\frac{\pi}{2}\]
\[ = 1\]
∴ \[\sin\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\} = 1\]