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**1. The problem statement, all variables and given/known data**

f(x)=sin^2(x)

**2. Relevant equations**

**3. The attempt at a solution**

solving for a(0)= i did (1/2Pi)*int(sin^2(x),x,-Pi..Pi)=1/2

b(n)=0 because sin^2(x) is an even function

a(n)=(1/Pi)*int(sin^2(x)cos(n*x),x,-Pi..Pi)=1/2Pi((sin(xn)/n)-(.5sin((2-n)x)/(2-n))-(.5sin((2+n)x)/(2+n))) this whole thing evaluated from -Pi..Pi

I keep getting zero although I know this is not the answer, so maybe I am messing up somewhere. Help is greatly appreciated.