> 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).