Verify that $\sin (A + B) + \sin (A - B) = 2 \sin A \sin B$ ?

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Solution

Verifying the given expression:
L.H.S
$= \sin (A + B) + \sin (A - B)$
$= \sin A \cos B + \cos A \sin B + \sin A \cos B - \cos A \sin B$
$= \sin A \cos B + \sin A \cos B$
$= 2 \sin A \cos B$
R.H.S
$= 2 \sin A \cos B$
Hence, L.H.S = R.H.S

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