The value of the integral \( \int_{0}^{\pi} \frac{\sin \left(n+\fra...

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The value of the integral \( \int_{0}^{\pi} \frac{\sin \left(n+\frac{1}{2}\right) x}{\sin x / 2} d x(n \in N) \)
\( \mathrm{P}^{142} \) is
(1) \( \pi \)
(2) \( 2 \pi \)
(3) \( 3 \pi \)
(4) None of these
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