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Question

In any ΔABC, 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
81
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Solution

The correct options are
B 9
C 27
D 3
(sin2A+sinA+1sinA)(sin2B+sinB+1sinB)(sin2C+sinC+1sinC)
(sinA+1sinA+1)(sinB+1sinB+1)(sinC+1+1sinC)
1x+x2>0
1+1x+x3
the whole term is greater than 27

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