Date: Mar 27, 2001 4:01 PM
Author: Antreas P. Hatzipolakis
Subject: Re: [HM] Theorem of tangents


Francine F. Abeles wrote:

> I'm interested in finding a reference in English to the origin
> and use of the theorem of tangents:
>
> (a-b)/(a+b) = tan (A-B)/2 x tan C/2, where a,b are the
> sides of a triangle; A,B,C are its angles.


We get the tan formula:

b - c
----- = tan(A/2) * tan((B-C)/2) [and cyclically]
b + c

from these ones, which are known as "Mollweide Formulae"

b - c
----- * cos(A/2) = sin((B-C)/2)
a

b + c
----- * sin(A/2) = cos((B-C)/2)
a

Karl Brandan Mollweide (1774 - 1825) published his formulae in a
paper on plane and spheric trigonometry (in 1808, I think).

Antreas