1. \frac{x}{\sqrt{1+x^{2}}}
  2. \frac{1}{\sqrt{1+x^{2}}}
  3. \frac{\sqrt{1+x^{2}}}{x}
  4. \sqrt{1+x^{2}}

Answers (1)

Let \cot ^{-1}x = \Theta

\Rightarrow \cot\Theta = x

Using Pythagoras theorem, \sin \Theta =\frac{1}{\sqrt{1+x^2}}

\Rightarrow \Theta =\sin ^{-1} \left ( \frac{1}{\sqrt{1+x^2}} \right )

\sin \left ( \sin ^{-1} \left ( \frac{1}{\sqrt{1+x^2}} \right ) \right ) = \frac{1}{\sqrt{1+x^2}}

Option (2) is correct

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