This makes no sense. bn cannot depend on x. Do you mean this is the integral of sin(nx)sin(x/3)beforeyou evaluate at the limits of integration?

How do you get that? When n= 1, for example, that givesNow I only need to put the limits in. The trouble is when i put the limits [-pi,pi) into the equation I get 0 which is not the answer!

at and evaluating at gives the negative of that so the difference is .

and this can't be true! The left side depends on x and the right side doesn't!and the next part of the question states:

show for all x E (-pi,pi)

sin (x/3) = (((9)(3^.5))/pi)(((-1)^n)n)/(1-9n^2))

I think I may need to use Dirichlets theorem however I need the answer to the part of the question before!