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a
< 1
b
>1
c
>1 but not >2
d
>1 but not >3/2
answer is D.
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Detailed Solution
cosA+cosB+cosC=1+4sinA2sinB2sinC2>1as neither of sinA2,sinB2,sinC2 is -ive or zero again cosA+cosB+cosC =2cosA+BCcosA−B2+1−2sin2C2≤2sinC2.1+1−2sin2C2 1+4sinA2sinB2sinC2≤32⇒cosA+cosB+cosC≤32