$<=>2 cos \frac{A+B}{2}.cos \frac{A-B}{2}+1-2 sin^{2}\frac{C}{2} = \frac{3}{2}$
$
<=>sin^{2} \frac{C}{2}- sin \frac{C}{2} . cos \frac{A-B}{2} + \frac{1}{4} = 0$
$<=>(sin \frac{C}{2} - \frac{1}{2} cos \frac{A-B}{2})^{2}+\frac{1}{4} sin^{2} \frac{A-B}{2} =0$
=>C=60,A=B