Hi everyone.

I'm hoping someone can help me out with this problem:

If f(x) and g(x) are any two distinct options from {1, cos x, sin x, cos 2x, sin 2x, cos 3x, sin 3x,...., cos nx, sin nx}

show that the integral from [-pi, pi] of f(x)g(x) is zero while the integral from [-pi, pi] of (f(x))^2 is non-zero.

Would I need to use trig identities? I don't really know where to get started.

Any help is much appreciated