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