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Question

If α,β,γ[0,π2], then the value of sin(α+β+γ)sinαsinβ+sinγ is

A
1
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B
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C
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D
None of these
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Solution

The correct option is B None of these
The value of sin(α+β+γ) is
=sinα+sinβ+sinγsinαcosβcosγcosαsinβcosγcosαcosβsinγ+sinαsinβcosγ
Therefore, sinα+sinβ+sinγ>sin(α+β+γ)
sin(α+β+γ)sinα+sinβ+sinγ<1

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