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De Moivre's Theorem states that if z = cos(q)+isin(q), then
zn = (cos(q)+isin(q))n = cos(nq)+isin(nq)
But then
z-n = cos(-nq)...
At GCSE level, proof questions are relatively rare and largely will all require a similar sort of approach. The difference with A Level is that the syllabus contains more than one method of proof. You wil...
If you look at the Taylor series expansion of ex: ex = 1 + x + x2/(2!) + x3/(3!) + x4/(4!)...
If you then make this eix, ...
The easiest way of approaching this question is to use De Moivre's formula: e^(inx) = cos(nx) + isin(nx) from which it is simple to show that cos(nx) = (e^(inx) + e^(-inx)) / 2 and sin(nx) = (e^(inx))- e^...
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
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