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Question

lf in triangle ABC,2cosAa+cosBb+2cosCc=abc+bca, then the value of the angle A, in degrees is

A
30
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B
60
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C
90
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D
120
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Solution

The correct option is B 90
cosA=b2+c2a22bc,cosB=a2+c2b22ac,

cosC=a2+b2c22ab

2(b2+c2a2)2abc+a2+c2b22abc+2(a2+b2c2)2abc=a2+b2abc

2b2+2c22a2+a2+c2b2+2a2+2b22c22=a2+b2

3b2+a2+c2=2a2+2b2

a2=b2+c2

A=π2

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