Chapter 5 - Trigonometric Identities - Section 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 208: 6

$\tan^{2}\theta+1=\sec^{2}\theta$

Since $\sin^2\theta+\cos^2\theta=1$ Dividing by $\cos^2\theta$ $\frac{ \sin^2\theta+\cos^2\theta } {\cos^2\theta}=\frac{1}{ \cos^2 \theta}$ $\frac{\sin^2\theta}{\cos^2\theta}+\frac{\cos^2\theta}{\cos^2 \theta}=\sec^2\theta$ $\tan^2\theta+1=\sec^2\theta$