\( J_{n}=\int_{0}^{\pi / 2}\left(\frac{\sin n x}{\sin x}\right)^{2} d x \) and \( I_{n}=\int_{0}....
\( J_{n}=\int_{0}^{\pi / 2}\left(\frac{\sin n x}{\sin x}\right)^{2} d x \) and \( I_{n}=\int_{0}^{\pi / 2} \frac{\sin (2 n+1) x}{\sin x} d x \)
\( \mathrm{P} \)
Then
(1) \( J_{n+1}-J_{n}=I_{n} \)
(2) \( J_{n}=I_{n+1}-I_{n} \)
(3) \( J_{n}=\frac{n \pi}{2} \)
(4) \( J_{n}=\frac{\pi}{2} \)
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