48
If $A = 60^\circ$ and $B = 30^\circ$, verify that : $\sin (A + B) = \sin A \cos B + \cos A \sin B$
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Sol. LHS = $\sin (60^\circ + 30^\circ) = \sin 90^\circ = 1$
RHS = $\sin 60^\circ \cos 30^\circ + \cos 60^\circ \sin 30^\circ$
$= \frac{\sqrt{3}}{2} \times \frac{\sqrt{3}}{2} + \frac{1}{2} \times \frac{1}{2} = 1$
$\therefore$ LHS = RHS
RHS = $\sin 60^\circ \cos 30^\circ + \cos 60^\circ \sin 30^\circ$
$= \frac{\sqrt{3}}{2} \times \frac{\sqrt{3}}{2} + \frac{1}{2} \times \frac{1}{2} = 1$
$\therefore$ LHS = RHS