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If in DeltaABC,(2cosA)/(a)+(cosB)/(b)+(2...

If in `DeltaABC,(2cosA)/(a)+(cosB)/(b)+(2cosC)/(c)=(a)/(bc)+(b)/(ca)`, then `angleA` is equal to

A

`90^(@)`

B

`45^(@)`

C

`60^(@)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(2cosA)/(a)+(cosB)/(b)+(2cosC)/(c)=(a)/(bc)+(b)/(ca)`
`=(2(b^(2)+c^(2)-a^(2)))/(2bca)+(c^(2)+a^(2)-b^(2))/(2bac)+(2(a^(2)+b^(2)-c^(2)))/(2abc)`
`=(a^(2)+b^(2))/(abc)`
`=2b^(2)+2c^(2)-2a^(2)+c^(2)+a^(2)b^(2)+2a^(2)+2b^(2)-2c^(2)`
`=2a^(2)+2b^(2)`
`=3b^(2)+c^(2)+a^(2)=2a^(2)+2b^(2)orb^(2)+c^(2)=a^(2)`
Hence , `angleA=90^(@)`.
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