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Topic: [HM] Theorem of tangents
Replies: 5   Last Post: Mar 28, 2001 4:57 PM

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 Antreas P. Hatzipolakis Posts: 940 Registered: 12/3/04
Re: [HM] Theorem of tangents
Posted: Mar 27, 2001 4:01 PM

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