Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.3 Verify Trigonometric Identities - 14.3 Exercises - Skill Practice - Page 928: 38

See below.

If we divide both sides of $\sin^2\theta+\cos^2\theta=1$ by $\sin^2\theta$ we get: $1+\cot^2\theta=\csc^2\theta.$ If we divide both sides of $\sin^2\theta+\cos^2\theta=1$ by $\cos^2\theta$ we get: $1+\tan^2\theta=\sec^2\theta.$