Let [itex]\alpha,\beta\in]0;\pi/2[[/itex]. Prove that [itex]\sin(\alpha+\beta)<\sin\alpha+\sin\beta[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

My intuition says it's true, as can be seen from [itex]\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta[/itex], because [itex]0<\cos\alpha,\cos\beta<1[/itex], but I haven't been able to prove it.

Thanks in advance!!!

- Kamataat

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# Homework Help: Trig proof question

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