What is a non-geometric proof to prove the sine addition formula?

Question

I know that method that using euler's constant or taylor's series works, but is there any others?

Search the google with the "non-geometric proof of sine addition formula" only provide me with the geometric way...

Anybody want to answer?

If you are given a geomtric definition then the proof is also geometric. — Belgi, Oct 01 '12 at 22:07
@Belgi - Any of the definition on http://mathworld.wolfram.com/Sine.html — Victor, Oct 01 '12 at 22:11
Did you study calculus before ? some of the definitions are with power series — Belgi, Oct 01 '12 at 22:12
@Belgi - Except the euler's constant and taylor's series method... — Victor, Oct 01 '12 at 22:15
@Victor perhaps http://math.stackexchange.com/questions/189016/deriving-the-addition-formula-of-sin-u-from-a-total-differential-equation/189101#189101 will be of interest. In that thread we discuss definitions of sine... this sort of question always comes back to that. — James S. Cook, Oct 02 '12 at 00:41

score 1 · Accepted Answer · answered Jun 12 '13 at 06:58

Here is a non-geometric proof of DeMoivre's theorem that does not use Euler's theorem. But the result of section 3 (before DeMoivre's theorem is proved) is the angle addition formulas, if you equate components: http://www.dfcd.net/articles/demoivre.pdf

What is a non-geometric proof to prove the sine addition formula?

1 Answers1