Domain and Range of Basic Inverse Trigonometric Functions
The minimum v...
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+sinγ≤0
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Solution
The correct option is Dsinα+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.