I'm studying Fourier series and came across this peculiar problem. I just studied (along with proper reasoning) that if $f(x)$ is an even function, then the fourier series has only Cosine terms and if it's an odd function then only Sine terms.
Now we here have an even function, and we're asked to find the Sine terms whereas it's expansion has only Cosine terms.
The question is: Show that the sine series of the constant function $f(x) = \pi/4$ is:
$$ \sin x+ \frac{1}{3}\sin 3x + \frac{1}{5}\sin5x + \ldots, \quad 0<x<\pi $$
What am I missing here?