I read that, for ##\delta>0##, if ##\delta<z\leq\pi##, then ##\sin\frac{z}{2}\geq\frac{2\delta}{\pi}##.(adsbygoogle = window.adsbygoogle || []).push({});

I cannot prove it. I know that ##\forall x\in\mathbb{R}\quad|\sin x|\leq |x|##, but that does not seem useful here...

Thank you so much for any help!

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# Trigonometric inequality

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