Answer 1

\[\cot^2 \theta - \tan^2 \theta\]

\[ = \left( {cosec}^2 \theta - 1 \right) - \left( \sec^2 \theta - 1 \right) \left( 1 + \tan^2 \theta = \sec^2 \theta   \& 1 + \cot^2 \theta = {cosec}^2 \theta \right)\]

\[ = {cosec}^2 \theta - 1 - \sec^2 \theta + 1\]

\[ = {cosec}^2 \theta - \sec^2 \theta\]