Chapter 6.2, Problem 79PE

Use the relationships $\frac{a}{c}=\frac{\sin A}{\sin C}$ and $\frac{b}{c}=\frac{\sin B}{\sin A}$ from the law the for law this of sines to show that $\frac{a+b}{c}=\frac{\cos \frac{A-B}{2}}{\sin \frac{C}{2}}$ . This is called a Mollweide equation, named after German mathematician and astronomer Karl Mollweide $\left(1774\text{-}1825\right)$ . Notice that the equation uses all six parts of a triangle, and for this reason, is sometimes used to check the solution to a triangle.