Find the value of  $$\frac{1 - \cot^2 \theta}{\tan^2 \theta - 1}$$

Correct option is C

Given:
Expression: $$\frac{1 - \cot^2 \theta}{\tan^2 \theta - 1}$$​​​

Formula Used:

​$$\cot^2 \theta = \frac{1}{\tan^2 \theta}$$​

Solution:

​$$\frac{1 - \cot^2 \theta}{\tan^2 \theta - 1} = \frac{1 - \frac{1}{\tan^2 \theta}}{\tan^2 \theta - 1}= \frac{\frac{\tan^2 \theta - 1}{\tan^2 \theta}}{\tan^2 \theta - 1}$$​​

= $$\frac{1}{\tan^2 \theta} = \cot^2 \theta$$​

Thus, the correct option is (c) $$\cot^2 \theta$$​