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I'm trying to calculate the Fourier Series for sin^{2}x on [-π, π]

For a_{0}I found 1/2. (By determining the average value of the function on the interval)

Since sin^{2}x is even, I know that b_{n}= 0.

Now, for a_{n}.. The following link shows the integral I used to try to evaluate a_{n}.

http://www.wolframalpha.com/...

Since a_{n}and b_{n}are both coming out to be zero, doesn't this imply that sin^{2}x = a_{0}= 1/2? Will someone please show me where I am going wrong? Can't find anything online about this. Everyone just always uses the sin^{2}identity and calls it good.

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# Fourier Series for (sin(x))^2

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