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Question
Wnte the value of the expression \[\tan\left( \frac{\sin^{- 1} x + \cos^{- 1} x}{2} \right), \text { when } x = \frac{\sqrt{3}}{2}\]
Solution
\[\tan\left( \frac{\sin^{- 1} x + \cos^{- 1} x}{2} \right) = \tan\left( \frac{\pi}{4} \right) \left[ \because \sin^{- 1} x + \cos^{- 1} x = \frac{\pi}{2} \right]\]
\[ = 1\]
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