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Question
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Solution
\[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right) = \sin^{- 1} 2 \times \frac{1}{2}\sqrt{1 - \left( \frac{1}{2} \right)^2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
\[ = \sin^{- 1} \frac{\sqrt{3}}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
\[ = \sin^{- 1} \left( \sin\frac{\pi}{3} \right) + \cos^{- 1} \left( \cos\frac{2\pi}{3} \right)\]
\[ = \frac{\pi}{3} + \frac{2\pi}{3}\]
\[ = \pi\]
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