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Find the value of  1−cot⁡2θtan⁡2θ−1\frac{1 - \cot^2 \theta}{\tan^2 \theta - 1}tan2θ−11−cot2θ​
Question

Find the value of  1cot2θtan2θ1\frac{1 - \cot^2 \theta}{\tan^2 \theta - 1}

A.

tan2θtan^2⁡θ​​

B.

tan θ

C.

cot2θcot^2⁡θ​​

D.

cot θ

Correct option is C

Given:
Expression: 1cot2θtan2θ1\frac{1 - \cot^2 \theta}{\tan^2 \theta - 1}​​​

Formula Used:

cot2θ=1tan2θ\cot^2 \theta = \frac{1}{\tan^2 \theta}

Solution:

1cot2θtan2θ1=11tan2θtan2θ1=tan2θ1tan2θtan2θ1\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}​​

1tan2θ=cot2θ\frac{1}{\tan^2 \theta} = \cot^2 \theta

Thus, the correct option is (c) cot2θ\cot^2 \theta


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