Using Euler's Formula to prove Sum and Difference Formulas?

I need to prove sin(x+y)=sinxcosy+cosxsiny, and the wikipedia article on this says that the quickest way to prove that formula is with Euler's Formula, e^(ix)=cosx+isinx, where e is the natural log, 2.71, and i is the imaginary number. How would I go about this? Is there a simpler way to solve the sum and difference formulas for sine and cosine? Thank you!