Mathematics · JEE | INVERSE TRIGONOMETRIC FUNCTIONS

The derivative or simplification of \( \sin(\tan^{-1} x) \) for \( |x| < 1 \) results in which of the following algebraic expressions?

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Correct answer · Option A

\( \frac{x}{\sqrt{1 + x^2}} \)

Let \( \theta = \tan^{-1} x \), so \( \tan\theta = x \). Then \( \sin\theta = \frac{\tan\theta}{\sqrt{1+\tan^2\theta}} = \frac{x}{\sqrt{1+x^2}} \).