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Question

If α,β,γϵ(0,π2), then sin(α+β+γ)sinα+sinβ+sinγ is-

A
<1
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B
>1
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C
=1
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D
<0
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Solution

The correct option is B <1
We know, 1<sin(α+β+γ)<1,sin(α+β+γ)=sin(α)cos(β)cos(γ)+cos(α)sin(β)cos(γ)+cos(α)cos(β)sin(γ)sin(α)sin(β)sin(γ)3<sinα+sinβ+sinγ<3,sin(α+β+γ)sinα+sinβ+sinγ<1

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