If \( \theta=\cot ^{-1} \sqrt{\cos x}-\tan ^{-1} \sqrt{\cos x} \), then \( \sin \theta= \) (a) \...

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If \( \theta=\cot ^{-1} \sqrt{\cos x}-\tan ^{-1} \sqrt{\cos x} \), then \( \sin \theta= \)
(a) \( \tan \frac{x}{2} \)
(b) \( \tan ^{2}\left(\frac{x}{2}\right) \)
(c) \( \frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right) \)
(d) None of these
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