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b)
$I=\int\limits_{-\pi}^{\pi}\cos mx\cos nxdx$
$=\int\limits_{-\pi}^{\pi} \frac{1}{2}(\cos(m+n)x+\cos(m-n)x)dx$
+ Nếu $m=n$
$I=\int\limits_{-\pi}^{\pi} \frac{1}{2}(\cos2mx+1)dx=\left[ { \frac{1}{4}\sin2mx+\frac{1}{2}x} \right]_{-\pi}^{\pi}=\pi$
+ Nếu $m=-n$
$I=\int\limits_{-\pi}^{\pi} \frac{1}{2}(\cos2mx+1)dx=\left[ { \frac{1}{4}\sin2mx+\frac{1}{2}x} \right]_{-\pi}^{\pi}=\pi$
+ Nếu $m\ne \pm n$
$I=\frac{1}{2}(\frac{\sin(m+n)x}{m+n}+\frac{\sin(m-n)x}{m-n})dx\left|\begin{array}{l}\pi\\-\pi\end{array}\right.=\frac{\sin(m+n)\pi}{m+n}+\frac{\sin(m-n)\pi}{m-n}$
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