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Question

In Δ ABC the sides opposite to angles A,B,C are denoted by a,b,c respectively.
If sinA4=sinB5=sinC6,

then value of cosA+cosB+cosC is equal to?

A
415
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B
113
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C
215
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D
2316
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Solution

The correct option is D 2316
Using sine rule, we get
sinAa=sinBb=sinCc
And it is given that
sinA4=sinB5=sinC6
Comparing both the expressions, we get
a=4, b=5, c=6.
Hence
cosA=b2+c2a22bc
=25+361660
=34.
Similarly cosB=916
cosC=18
Hence
cosθ
=34+18+916
12+2+916
=2316.

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