Express $tan (a r c sin (x))$ without trigonometric functions.

\frac{1}{x}

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\sqrt{1 - x^{2}}

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

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\frac{x}{\sqrt{1 - x^{2}}}

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none of these

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Solution

The correct option is D $\frac{x}{\sqrt{1 - x^{2}}}$
Using Pythagoras theorem,
$tan (a r c sin (x))$
$= tan ({tan}^{- 1} \frac{x}{\sqrt{1 - x^{2}}})$
$= \frac{x}{\sqrt{1 - x^{2}}}$

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