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

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

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...

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How do you define the $\sin$ function ? –  Belgi Oct 1 '12 at 22:05
@Belgi - The most basic one in High School. –  Victor Oct 1 '12 at 22:06
If you are given a geomtric definition then the proof is also geometric. –  Belgi Oct 1 '12 at 22:07
@Belgi - Any of the definition on mathworld.wolfram.com/Sine.html –  Victor Oct 1 '12 at 22:11
@Victor perhaps math.stackexchange.com/questions/189016/… 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 2 '12 at 0:41

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

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