(D) Let $\theta = \cot ^{ - 1}x$. Then,$\cot \theta = x = \frac{x}{1}$.We know that $\csc^2 \theta = 1 + \cot^2 \theta = 1 + x^2$.Therefore,$\csc \the

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(D) Let $\theta = \cot ^{ - 1}x$. Then,$\cot \theta = x = \frac{x}{1}$.We know that $\csc^2 \theta = 1 + \cot^2 \theta = 1 + x^2$.Therefore,$\csc \theta = \sqrt{1 + x^2}$.Since $\sin \theta = \frac{1}{\csc \theta}$,we have $\sin \theta = \frac{1}{\sqrt{1 + x^2}}$.Thus,$\sin (\cot ^{ - 1}x) = \frac{1}{\sqrt{1 + x^2}} = (1 + x^2)^{-1/2}$.