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Prove Euler's identity and get practice with Taylor expansions of key functions (sine, cosine,


Prove that exp(iθ) = cosθ + i sinθ by using the Taylor expansions:

exp(x) = 1 + x + x^2/2 + x^3/3! + x^4/4!+ ...

cos(x) = 1-x^2/2 + x^4/4 + ...

sin(x) = x - x^3/3!+...

[Hint: Taylor both sides of this equation and show that they are indeed equal to each other.]

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