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　実数$a$，$b$ $\displaystyle \left( 0 \leqq a < \frac{\pi}{4} , 0 \leqq b < \frac{\pi}{4} \right)$に対し
次の不等式の成り立つことを示せ．
\[ \sqrt{\tan a \cdot \tan b} \leqq \tan \left( \frac{a+b}{2} \right) \leqq \frac{1}{2}(\tan a + \tan b) \]
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