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Question

If α,β,γϵ(0,π2), then sin(α+β+γ)sinα+sinβ+sinγ<a
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Solution

sin(α+β+γ)=sinαcosβcosα+cosαsinβcosγ+cosαcosβsinγsinαsinβsinγ
or sin(α+β+γ)sinαsinβsinγ=sinα(cosβcosγ1)+sinβ(cosγcosγ1)+sinγ(cosαcosβ1)sinαsinβsinγ
or sin(α+β+γ)sinαsinβsinγ<0
or sin(α+β+γ)<sinα+sinβ+sinγ
or sin(α+β+γ)sinα+sinβ+sinγ<1
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