# $[\operatorname{Cos}(x)+i\operatorname{Sin}(x)]\cdot[\operatorname{Cos}(y)+i\operatorname{Sin}(y)]=\operatorname{Cos}(x+y)+i\operatorname{Sin}(x+y)$

Had this non-analytic theorem ever been known before Euler discovered his analytic formula: $$\operatorname{Cos}(x)+i\operatorname{Sin}(x)= e^{ix}$$ ?

Please notice the distinction between, the theorem indicated in the title, and De Moivre's theorem - which is not about a sum of angles.

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