(C) Let $\sin^{-1}x = \theta$. Then,$\sin \theta = x$. We know that $1 + \cot^2 \theta = \csc^2 \theta$. Since $\csc \theta = \frac{1}{\sin \theta}$,w

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