Which of the identities given below is NOT true?

Correct option is D

Solution

analyze each option

option(a) $$sec^2\theta-tan^2\theta=1$$

The equation $$sec^2\theta-tan^2\theta=1$$ is identity in trigonometry

thus ,it is correct formula 

option(b) $$cosec^2\theta-cot^2\theta=1$$

It is another equation $$cosec^2\theta-cot^2\theta=1$$ is identity in trigonometry

thus, it is correct formula

option(c) $$sin^2\theta+cos^2\theta=1$$

This is an equation $$sin^2\theta+cos^2\theta=1$$  is identity in trigonometry

thus, it is correct formula

option(d)  

​$$tan^2\theta+cot^2\theta=1$$ is not a true identity for all values of $$\theta$$.and not a general trigonometric identity .

thus, option (d) is a correct answer