If α,β,γϵ(0,π2), then sin(α+β+γ)sinα+sinβ+sinγ<a Find a
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Solution
sin(α+β+γ)=sinαcosβcosα+cosαsinβcosγ+cosαcosβsinγ−sinαsinβsinγ or sin(α+β+γ)−sinα−sinβ−sinγ=sinα(cosβcosγ−1)+sinβ(cosγcosγ−1)+sinγ(cosαcosβ−1)−sinαsinβsinγ or sin(α+β+γ)−sinα−sinβ−sinγ<0 or sin(α+β+γ)<sinα+sinβ+sinγ or sin(α+β+γ)sinα+sinβ+sinγ<1 Ans: 1