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Q. $\frac{\sin A - \sin B}{\cos A + \cos B} $ is equal to

KEAMKEAM 2018

Solution:

Given that,
$\frac{\sin A-\sin B}{\cos A+\cos B}$
$=\frac{2 \sin \left(\frac{A-B}{2}\right) \cos \left(\frac{A+B}{2}\right)}{2 \cos \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)}$
$=\frac{\sin \left(\frac{A-B}{2}\right)}{\cos \left(\frac{A-B}{2}\right)}=\tan \left(\frac{A-B}{2}\right)$