For $0 < \mathrm{a} < 1$, the value of the integral $\int_\limits0^\pi \frac{\mathrm{d} x}{1-2 \mathrm{a} \cos x+\mathrm{a}^2}$ is :

Question

$\frac{\pi^2}{\pi+a^2}$

$\frac{\pi^2}{\pi-a^2}$

$\frac{\pi}{1-\mathrm{a}^2}$

$\frac{\pi}{1+\mathrm{a}^2}$

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