Chapter 1: Functions - Section 1.3 - Trigonometric Functions - Exercises 1.3 - Page 28: 35

$\cos{(A-B)} = \cos{A} \cos{B} + \sin{A} \sin{B} = \text{ RHS}$

Addition formula $$\cos{(A+B)}= \cos{A} \cos{B}-\sin{A}\sin{B}$$ $\therefore \cos{(A-B)} = \cos{A} \cos{(-B)} - \sin{A} \sin{(-B)}$ $\cos{(A-B)} = \cos{A} \cos{B} - \sin{A} (-\sin{B})$ $\cos{(A-B)} = \cos{A} \cos{B} + \sin{A} \sin{B} = \text{ RHS}$