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Further Mathematics
A Level
Express cos(4x) in terms of powers of cos(x)
By quoting De Moivre's theorem, (r(cos(x) + isin(x)))n = rn(cos(nx) + isin(nx)), we can realise that cos(4x) is a result of the real parts of (cos(x) + isin(x))4
Prove e^(ix) = cos (x) + isin(x)
We first write each side of the equation using the maclaurin series for each function.
eix = 1 + ix + (ix)2/2! + (ix)3/3! + (ix)4/4! + ......
