Chapter 5 - Trigonometric Identities - Section 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 210: 94

The following statement is an identity: $1+cot^2~x = \frac{sec^2~x}{sec^2~x-1}$

We can see that the graph of $~~y = 1+cot^2~x~~$ is the same as the graph of $~~y = \frac{sec^2~x}{sec^2~x-1}$ Therefore, the following statement is an identity: $1+cot^2~x = \frac{sec^2~x}{sec^2~x-1}$