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\( \tan ^{-1}(\tan \theta)=\left\{\begin{array}{cc}\pi+\theta, & -\frac{3 \pi}{2}\theta-\frac{\pi}{2} \\ \theta, & -\frac{\pi}{2}\theta\frac{\pi}{2} \\ -\pi+\theta, & \frac{\pi}{2}\theta\frac{3 \pi}{2}\end{array}\right. \),
\( \mathrm{P} \)
W
\[
\begin{array}{c}
\sin ^{-1}(\sin \theta)=\left\{\begin{array}{cc}
-\pi-\theta, & -\frac{3 \pi}{2} \leq \theta-\frac{\pi}{2} \\
\theta, & -\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2} \\
\pi-\theta, & \frac{\pi}{2}\theta \leq \frac{3 \pi}{2}
\end{array} .\right. \\
\cos ^{-1}(\cos \theta)=\left\{\begin{array}{ccc}
-\theta, & -\pi \leq \theta0 \\
\theta, & 0 \leq \theta \leq \pi \\
2 \pi-\theta, & \pi\theta \leq 2 \pi
\end{array}\right.
\end{array}
\]
Based on the above results, answer each of the following :
\( \cos ^{-1} \mathrm{x} \) is equal to
(A) \( \sin ^{-1} \sqrt{1-x^{2}} \) if \( -1x1 \)
(B) \( -\sin ^{-1} \sqrt{1-x^{2}} \) if \( -1x0 \)
(C) \( \sin ^{-1} \sqrt{1-x^{2}} \) if \( -1x0 \)
(D) \( \sin ^{-1} \sqrt{1-x^{2}} \) if \( 0x1 \)
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