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