If 0

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(C) Let $x = \cos 	heta$. Since $0 < x < 1$,we have $	heta \in (0, \pi/2)$.Substituting $x = \cos 	heta$ into the expression:$\cot ^{-1}\left( \fra

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$2\cos ^{-1}x$

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(C) Let $x = \cos 	heta$. Since $0 Substituting $x = \cos 	heta$ into the expression:$\cot ^{-1}\left( \frac{2\cos ^2 	heta - 1}{2\cos 	heta \sqrt{1 - \cos ^2 	heta}} ight)$$= \cot ^{-1}\left( \frac{\cos 2	heta}{2\cos 	heta \sin 	heta} ight)$$= \cot ^{-1}\left( \frac{\cos 2	heta}{\sin 2	heta} ight)$$= \cot ^{-1}(\cot 2	heta)$Since $	heta \in (0, \pi/2)$,then $2	heta \in (0, \pi)$.Thus,$\cot ^{-1}(\cot 2	heta) = 2	heta = 2\cos ^{-1}x$.

If $0 < x < 1$,then $\cot ^{-1}\left( \frac{2x^2 - 1}{2x\sqrt{1 - x^2}} \right)$ is equal to

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