Evaluate: tan^{-1} left( frac{1}{sqrt{x^2 - 1 | vedclass

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(C) Let $x = \csc 	heta$,where $	heta \in [-\frac{\pi}{2}, 0) \cup (0, \frac{\pi}{2}]$.Then $	heta = \csc^{-1} x$.Substituting this into the expres

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$\csc^{-1} x$

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(C) Let $x = \csc 	heta$,where $	heta \in [-\frac{\pi}{2}, 0) \cup (0, \frac{\pi}{2}]$.Then $	heta = \csc^{-1} x$.Substituting this into the expression:$	an^{-1} \left( \frac{1}{\sqrt{\csc^2 	heta - 1}} ight) = 	an^{-1} \left( \frac{1}{\sqrt{\cot^2 	heta}} ight)$$= 	an^{-1} \left( \frac{1}{|\cot 	heta|} ight)$.Assuming $x > 1$,$	heta$ is in $(0, \frac{\pi}{2}]$,so $\cot 	heta > 0$.$= 	an^{-1} (	an 	heta) = 	heta = \csc^{-1} x$.

Evaluate: $\tan^{-1} \left( \frac{1}{\sqrt{x^2 - 1}} \right)$

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