Correct option is CGiven:Expression: 1−cot2θtan2θ−1\frac{1 - \cot^2 \theta}{\tan^2 \theta - 1}tan2θ−11−cot2θFormula Used:cot2θ=1tan2θ\cot^2 \theta = \frac{1}{\tan^2 \theta}cot2θ=tan2θ1Solution:1−cot2θtan2θ−1=1−1tan2θtan2θ−1=tan2θ−1tan2θtan2θ−1\frac{1 - \cot^2 \theta}{\tan^2 \theta - 1} = \frac{1 - \frac{1}{\tan^2 \theta}}{\tan^2 \theta - 1}= \frac{\frac{\tan^2 \theta - 1}{\tan^2 \theta}}{\tan^2 \theta - 1}tan2θ−11−cot2θ=tan2θ−11−tan2θ1=tan2θ−1tan2θtan2θ−1= 1tan2θ=cot2θ\frac{1}{\tan^2 \theta} = \cot^2 \thetatan2θ1=cot2θThus, the correct option is (c) cot2θ\cot^2 \thetacot2θ