Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.3 Verify Trigonometric Identities - 14.3 Exercises - Skill Practice - Page 928: 29

See below.

Using the given identities: $\frac{\csc^2\theta-\cot^2\theta}{1-\sin^2\theta}=\frac{\frac{1}{\sin^2\theta}-\frac{\cos^2\theta}{\sin^2\theta}}{\cos^2\theta}=\frac{\frac{1-\cos^2\theta}{\sin^2\theta}}{\cos^2\theta}=\frac{\frac{\sin^2\theta}{\sin^2\theta}}{\cos^2\theta}=\frac{1}{\cos^2\theta}=\sec^2\theta$ Hence we showed what we had to.