\( \Large \frac{\cot^{2} \theta +1}{\cot^{2}\theta -1}=\frac{1+\tan^{2}\theta }{1-\tan^{2} \theta } \) =\( \Large \frac{1}{\cos^{2} \theta -\sin^{2} \theta } = \frac{1}{\cos 2 \theta } = \sec 2 \theta \)