Chapter 6 - Analytic Trigonometry - Section 6.4 Trigonometric Identities - 6.4 Assess Your Understanding - Page 497: 27

$\text{See the steps}$

$\text{ LHS } = (\sec{\theta}-1)(\sec{\theta}+1)$ $\text{By Expanding:}$ \begin{align} \text{ LHS } & = \sec^2{\theta}-\sec{\theta}+\sec{\theta}-1 \\[2mm] &= \sec^2{\theta}-1 \\[2mm] &= \tan^2{\theta} \\[2mm] & = \text{ RHS} \end{align}