(Solved): (a) Show that {cos(2x), sin(2x)} is an orthonormal family with respect to the inner product 2 TT 1 ...

(a) Show that {cos(2x), sin(2x)} is an orthonormal family with respect to the inner product 2 TT 1 (8,9) - - I f(t)g(t) dt. T -TT - (b) Use Part (a) to find the function f(x) = a cos(2x) +b sin(2x) which makes the quantity 7T JCD) = ["\1 +2x – f(x)]* dx ( - 1 + -TT as small as possible.