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\item[(1)]$\displaystyle0\leqq\alpha<\beta\leqq\frac{\pi}{2}$であるとき，次の不等式を示せ．
\[ \int_\alpha^\beta \sin xdx + \int_{\pi-\beta}^{\pi-\alpha} \sin xdx >
(\beta-\alpha)(\sin\alpha+\sin(\pi-\beta)) \]
\item[(2)]$\displaystyle\sum_{k=1}^7\sin\frac{k\pi}{8}<\frac{16}{\pi}$を示せ．
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