Evaluate: cos-1(1/2) + 2sin-1(1/2)
Solution:
We know:
\[ \cos^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{3} \]
\[ \sin^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{6} \]
Substitute values:
\[ \cos^{-1}\left(\frac{1}{2}\right) + 2\sin^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{3} + 2 \times \frac{\pi}{6} \]
\[ = \frac{\pi}{3} + \frac{\pi}{3} = \frac{2\pi}{3} \]
Final Answer:
Value = \[ \frac{2\pi}{3} \]