1. The Fourier expansion for any (reasonable) function may be written do + NTT f (2) = 2 an Cos ("Tax) + 2 on sin L -x) n= n=1 (a) Given this expansion, prove that +L aj = dx f (x) cos L L L +L bj = 1 L dx f (x) sin J TT L "x) (While it doesn't affect the math, use L = 7 for convenience.) (b) Show that for even functions (f(-x) = f(x)), bn = 0 for all n, and that for odd functions (f (-x) = -f(x)), an = 0 for all n