a) Verify that the set of functions 1, cos x, cos 2x,... forms an orthogonal system on the interval [0, ]. b) Verify that the set of functions COS ' n = 0, 1, 2..., form an orthogonal system on the interval [0, 1]. c) If f(x) = Cn COS (NTT) n=0 in the mean-square sense on [0,1], what is the formula for the cn? This series is called the Fourier cosine series for f on [0,1].