I encountered Mollweide's formula and I search the net for the proof.. I got this link Link . I studied the proof and it requires a lot of trigonometric identities. Can we have another means in proving this identity? A better approach? thanks a lot in advance..:)
By the way the Mollweide's formula is:
Given any triangle with $a,\ b,\ c, \ \alpha ,\ \beta, \ \gamma $.$$\frac{a+b}{c}= \frac{\cos (\frac{\alpha – \beta}{2})}{\sin (\frac{\gamma}{2})}$$ and
$$\frac{a-b}{c}= \frac{\sin (\frac{\alpha – \beta}{2})}{\cos(\frac{\gamma}{2})}$$
Best Answer
Screenshot from http://cartography.tuwien.ac.at/content07/index.php?download=Lapaine_Mollweide_draft_paper.pdf
Proof attributed to H. Arthur De Kleine, "Proof Without Words: Mollweide's Equation", Mathematics Magazine, volume 61, number 5, page 281, December, 1988.