Mollweide’s equations

[10pt]

In a triangle, having the sides $a$, $b$ and $c$ opposite to the angles $\alpha$, $\beta$ and $\gamma$ respectively the following equations hold:

$$(a+b)\sin \frac{\gamma }{2}=c\cos \left(\frac{\alpha -\beta }{2}\right)$$

and

$$(a-b)\cos \frac{\gamma }{2}=c\sin \left(\frac{\alpha -\beta }{2}\right).$$