Chapter 7 - Analytic Trigonometry - 7.5 Sum and Difference Formulas - 7.5 Assess Your Understanding - Page 488: 60

$2\cos{(\alpha)}\cos{(\beta)}$

Recall: (1) $\cos{(\alpha+\beta)}=\cos{(\alpha)}\cos{(\beta)}-\sin{(\alpha)}\sin{(\beta)}$ (2)$\cos{(\alpha-\beta)}=\cos{(\alpha)}\cos{(\beta)}+\sin{(\alpha)}\sin{(\beta)}$ Hence, $\cos{(\alpha+\beta)}+\cos{(\alpha-\beta)}\\=[\cos{(\alpha)}\cos{(\beta)}-\sin{(\alpha)}\sin{(\beta)}]+[(\cos{(\alpha)}\cos{(\beta)}+\sin{(\alpha)}\sin{(\beta))}]\\=2\cos{(\alpha)}\cos{(\beta)}.$