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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...

Anybody want to answer?

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    @JamesS.Coo$k$ - Any other way?2012-10-02

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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