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For \(0<\mathrm{a}<1\), the value of the integral \(\int_{0}^{\pi} \frac{\mathrm{d} x}{1-2 \mathrm{a} \cos x+\math…

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

[JEE Main 2024, 27 Jan (Shift 2)]

\(\frac{\pi}{1-\mathrm{a}^{2}}\)

\(\frac{\pi}{1+\mathrm{a}^{2}}\)

\(\frac{\pi^{2}}{\pi-a^{2}}\)

\(\frac{\pi^{2}}{\pi+a^{2}}\)

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For \(0&lt;\mathrm{a}&lt;1\), the value of the integral \(\int_{0}^{\pi} \frac{\mathrm{d} x}{1-2 \mathrm{a} \cos x+\math…