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The set of values of $x$ for which $\tan^{- 1} \frac{x}{\sqrt{1 - x^{2}}} = \sin^{- 1} x$ holds,

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[0, 1]

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Correct option is B

We observe that RHS is defined for all x∈[−1, 1]whereas LHS is meaningful for -1 < x < l.Also, for x∈(−1, 1), we havetan−1⁡x1−x2=tan−1⁡sin⁡θcos⁡θ, where x=sin⁡θ=θ=sin−1⁡x

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The set of values of x for which tan−1⁡x1−x2=sin−1⁡x holds,

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The set of values of $x$ for which $\tan^{- 1} \frac{x}{\sqrt{1 - x^{2}}} = \sin^{- 1} x$ holds,