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Question

If in ABC 2 cos Aa+cos Bb+2cos Cc=abc+bca= then A is equal to


A

90°

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B

45°

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C

60°

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D

None of these

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Solution

The correct option is A

90°


We have 2cos Aa+cos Bb+2cos Cc=abc+bca
or 2(b2+c2a2)2bca+c2+a2b22bac+2(a2+b2c2)2abc=a2+b2abc
2b2+2c22a2+c2+a2b2+2a2+2b2c2=2a2+2b2
or 3b2+c2+a2=2a2+2b2 or b2+c2=a2
Hence A=90o


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