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

Find the fourier series of f(x) = sin^2(x)

**2. Relevant equations**

bn = because f(x) is even

ao = (1/(2*∏))*∫(f(x)) (from 0 to 2*∏)

an = (1/(∏))*∫(f(x)*cos(x)) (from 0 to 2*∏)

**3. The attempt at a solution**

ao = (1/(2*∏))*∫(f(x)) (from 0 to 2*∏) = ao = 1/2

an = (1/(∏))*∫(f(x)*cos(x)) (from 0 to 2*∏) = sin^3(x) from 0 to 2∏ and I keep resulting in zero

the answer is to the fourier series I know is 1/2 - (cos(2x))/2 how to get the cos(2x)/2 part. Is there a trig identity I am missing?