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Binomial Theorem

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(a)Express e-½iθ-e½iθ in trigonometric form, and show that (1-eiθ)2 = -4eiθsin2 ½θ.

(b) For a positive integer n, series C and S are given by

where is binomial coefficient. By considering the expansion of
(1-y)2n show that C = (-4)n cos nθsin2n (½θ) , and find a similar expression
for S.

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