Question: Prove that if g(x) is an odd function and f(x) an even function of x, the product g(x)[c + f(x)] is an odd function if

Prove that if g(x) is an odd function and f(x) an even function of x, the product g(x)[c + f(x)] is an odd function if c is a constant. A periodic function with period 2π is defined by

in the interval –π ≤ θ ≤ π. Show that the Fourier series representation of the function is

F(0) = (-1)+1 n n=1 sin no

F(0) = 20(0)

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