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Question

In ABC, if A,B and C represent the angles of a triangle, then the maximum value of sinA2+sinB2+sinC2 is

A
12
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B
1
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C
32
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D
3
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Solution

The correct option is C 32
Let sinA2+sinB2+sinC2=k
2sinA+B4cosAB4+cosA+B2=k2sin2A+B42cosAB4sinA+B4+k1=0
Since, sinA+B4 is real
4cos2AB48(k1)02(k1)cos2AB41k32

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