Problem 1804 (difficulty: 4/10)

Let \(\displaystyle n\) be a positive integer and let \(\displaystyle -1<a<1\).

\(\displaystyle \int_{-\pi}^\pi \frac{\cos(nt)}{1-2a\cos t+a^2} \dt =? \qquad \int_{-\pi}^\pi \frac{\sin(nt)}{1-2a\cos t+a^2} \dt =? \)

Hint-->

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