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Question

In ΔABC,C=2π3, then the value of cos2A+cos2BcosA.cosB=___


A

12

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B

14

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C

34

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D

32

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Solution

The correct option is C

34


C=2π3A+B=π3
Now cos2A+cos2BcosAcosB=1+cos2A2+1+cos2B212[cos(A+B)+cos(AB)]
=12[2+2cos(A+B)cos(AB)]12[12+cos(AB)]=12[2+212cos(AB)]1412cos(AB)=114=34


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