(a) Draw the graph of $f(x) = |\cos x|$ in $(-\pi, \pi)$. Is it odd o…

Question

(a) Draw the graph of $f(x) = |\cos x|$ in $(-\pi, \pi)$. Is it odd or even function? Also expand it as a Fourier series in $(-\pi, \pi)$.

(b) Using Fourier Cosine series of $f(x) = (x - 1)^2$ for $x \in (0, 1)$, show that $\frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \ldots$

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