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Question

In any ABC, Π(sin2A+sinA+1sinA) is always greater than :

A
9
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B
3
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C
27
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D
none of these
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Solution

The correct option is D 27
Let y=Π(sin2A+sinA+1sinA)=Π[1+(sinA+1sinA)]
Now we know in any triangle all sinA,sinB,sinC are positive.
Thus using A.MG.MsinA+1sinA2
Hence yΠ(1+2)=27

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