Chapter 7 - Analytic Trigonometry - 7.5 Sum and Difference Formulas - 7.5 Assess Your Understanding - Page 488: 70

See below.

Step 1. $cos(\alpha-\beta)=cos(\alpha)cos(\beta)+sin(\alpha)sin(\beta)$ Step 2. $LHS=sec(\alpha-\beta)=\frac{1}{cos(\alpha-\beta)}=\frac{1}{cos(\alpha)cos(\beta)+sin(\alpha)sin(\beta)}\times\frac{\frac{1}{cos(\alpha)cos(\beta)}}{\frac{1}{cos(\alpha)cos(\beta)}}=\frac{sec(\alpha)sec(\beta)}{1+tan(\alpha)tan(\beta)}=RHS$