Question

Find the value of \[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right)\]

Answer 1

\[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right) = 2 \sec^{- 1} \left( \sec\frac{\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{\pi}{6} \right)\]
\[ = 2 \times \frac{\pi}{3} + \frac{\pi}{6}\]
\[ = \frac{5\pi}{6}\]