The value of \( \int_{0}^{\pi} \frac{\sin \left(n+\frac{1}{2}\right) x}{\sin \left(\frac{x}{2}\r...
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0The value of \( \int_{0}^{\pi} \frac{\sin \left(n+\frac{1}{2}\right) x}{\sin \left(\frac{x}{2}\right)} d x \) is
(A) \( \frac{\pi}{2} \)
(B) 0
(C) \( \pi \)
(D) \( 2 \pi \)
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