Question

Prove the following:
$\frac{sinx-siny}{cosx+cosy}=tan\frac{x-y}{2}$

Answer 1

$LHS=\frac{sinx-siny}{cosx+cosy}=\frac{2\cos \left(\frac{x+y}{2}\right)\sin \left(\frac{x-y}{2}\right)}{2\cos \left(\frac{x+y}{2}\right)\cos \left(\frac{x-y}{2}\right)}$

$=\tan \frac{x-y}{2}=RHS$

Hence, proved