Mollweide’s Formula For any triangle, Mollweide’s Formula (named after Karl Mollweide, 1774–1825) states that $\frac{a+b}{c}=\frac{\cos \left[{\displaystyle \frac{1}{2}}\left(A-B\right)\right]}{\sin \left({\displaystyle \frac{1}{2}}C\right)}$

Derive it.

[Hint: Use the Law of Sines and then a Sum-to-Product Formula. Notice that this formula involves all six parts of a triangle. As a result, it is sometimes used to check the solution of a triangle.]

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