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Question

The value of $\sin^{- 1} \{\cot [\sin^{- 1} \sqrt{\frac{2 - \sqrt{3}}{4}} + \cos^{- 1} (\frac{\sqrt{12}}{4}) + \sec^{- 1} \sqrt{2}]\}$ is

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Solution

Given expression
$\begin{array}{l} = \sin^{- 1} \cot \{\sin^{- 1} \sqrt{\frac{2 - \sqrt{3}}{4}} + \cos^{- 1} (\frac{\sqrt{3}}{2}) + \cos^{- 1} (\frac{1}{\sqrt{2}})] \\ = \sin^{- 1} \cot \{\sin^{- 1} \sqrt{\frac{2 - \sqrt{3}}{4}} + \cos^{- 1} \sqrt{\frac{2 - \sqrt{3}}{4}}\} \\ = \sin^{- 1} \{\cot \frac{π}{2}\} = \sin^{- 1} 0 = 0 \end{array}$

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If $- 1 < x < 0,$ then $\sin^{- 1} x$ equals

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