Obtain \(a_{n}=\frac{2}{T}\int_{0}^{T}{f\left( t \right)\cos \left( n\omega _{0}t \right)dt}\) and \(b_{n}=\frac{2}{T}\int_{0}^{T}{f\left( t \right)\sin \left( n\omega _{0}t \right)dt}\) with careful identification of all terms in the expression.
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add constant term discussion.