Need complete solutions to these two questions. Optional part not required

5, Verify that the trig-interpolation Q(x)=0.5(1+e/\\{inx})p(x) + 0.5(1-e/'{inx})q(x) match all data points exactly, where p(x) and q(x) only interpolates the even and odd data points, respectively. 6, (a) Calculate C_[0}/\\{(1)} without using C_{1}'\\{(1)} and symmetry. (b) Verify the second property of C_{i}"{(n)}, symmetry of the Newton-Cotes coefficients. (0) [Optional] Verify its first property by induction