Sure, this takes "[cos(x)]^2 + [sin(x)]^2 = 1" off the list, but doesn't it require you to put "cos(-x) = cos(x)" and "sin(-x) = -sin(x)" on it, to get "(cosθ-isinθ)" from "e^(-iθ)"?
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Only if you forget about how complex conjugation works. (e^-ix) = (e^ix)* = cos x - i sin x
As indicated in the other reply, think of the minus as changing the sign of i instead of x.