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Question

The minimum value of the expression sinα+sinβ+sinγ, where α,β,γ are real numbers satisfying α+β+γ=π is

A
sinα+sinβ+sinγ>0
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B
sinα+sinβ+sinγ<0
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C
sinα+sinβ+sinγ=0
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D
sinα+sinβ+sinγ0
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Solution

The correct option is D sinα+sinβ+sinγ>0
We have, α+β+γ=π
Also we know, if θ[0,π] then sinθ[0,1]
since α+β+γ=π so α,β,γ can't be zero together.
Thus sinα+sinβ+sinγ>0
Hence minimum value of sinα+sinβ+sinγ will be positive.

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