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Q.

In a triangle ABC, cosA+cosB+cosC

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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
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In a triangle ABC, cosA+cosB+cosC