Question

Help with Fourier series

Answer 1

I need to find the Fourier cosine series to \[f(x)=\cos(3x)\sin^2(x)\]
Because the series are 2π-periodic and even I can use this equation
\[f(x)=a_{0}+\sum_{n=1}^{∞}a_{n}\cos(nx)\]
Where
\[a_{0}=\frac{ 1 }{ π }\int\limits_{0}^{π}f(x)dx\]
and
\[a_{n}=\frac{ 2 }{ π }\int\limits_{0}^{π}f(x)\cos(nx)\]
Is it true?