6. [Fourier series as a Least Squares approximation for periodic functions] Let L?[0,21] be the inner product space of all real functions f such that 12" (f ())dx is finite with f.g= $* $(a)g(a)der (i) Show that S = {1, sin r, cost, sin(2.0), cos(2:0), ..

6. [Fourier series as a Least Squares approximation for periodic functions] Let L?[0,21] be the inner product space of all real functions f such that 12" (f ())dx is finite with f.g= $* $(a)g(a)der (i) Show that S = {1, sin r, cost, sin(2.0), cos(2:0), ... , sin(m1), cos(mr),... } is an orthogonal set. (ii) Given f(.1) E L?[0,21], by (i) let f(1) = 20 + = (ar, cos(n.) + bry sin(n.1)). Find do, Ara, bere