Chapter 7 - Analytic Trigonometry - 7.5 Sum and Difference Formulas - 7.5 Assess Your Understanding - Page 488: 69

See below.

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