(a). Determine the coefficient a(n) in each of the following Taylor's series expansions:
(i) sin x= ∞Σ(n=0) a(n)x^(2n+1)
(ii) cos x= ∞Σ(n=0) a(n)x^(2n)
(iii) e^x= ∞Σ(n=0) a(n)x^n
(b). From your results in part (a), derive a relation between e^(ix) and cosx + i sin x
where i^2 = −1.