Answer
See the steps.
Work Step by Step
$\sin{(A+B)} + \sin{(A-B)} = $
$$ \sin{A} \cos{B} + \cos{A} \sin{B} + \sin{A} \cos{B} - \cos{A} \sin{B} $$
$LHS = 2 \sin{A} \cos{B} = RHS$
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