### Binomial Theorem for Euler's Formula

(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.