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How can we learn all the trigonometric formulae with Euler's formula?
And how does that give us the formula for sine?
By subtracting the original equation from the second one, we get e^(ix) - e^(-ix) = 2i*sin(x). Solving for sin(x) gives us sin(x) = (e^(ix) - e^(-ix))/2i. And there you have it! The formula for sine using Euler's formula.