The set of values of x such that $\sin^{- 1} x - \cos^{- 1} x > 0$ are

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$x \in (1, \frac{1}{\sqrt{2}})$

$x \in (\frac{1}{\sqrt{2}}, - 1)$

$(\frac{1}{\sqrt{2}}, 1)$

$x \in (1 / \sqrt{2}, 1]$

answer is A.

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Detailed Solution

$\begin{array}{l} \sin^{- 1} x - \cos^{- 1} x > 0 \Rightarrow \sin^{- 1} x - (\frac{π}{2} - \sin^{- 1} x) > 0 \\ \Rightarrow \sin^{- 1} x > \frac{π}{4} \\ ∴ x \in (\frac{1}{\sqrt{2}}, 1) a s |x| \leq 1 \end{array}$

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