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ln a DeltaABC, if (cosA)/a=(cosB)/b=(cos...

ln a `DeltaABC`, if `(cosA)/a=(cosB)/b=(cosC)/c` and the side a = 2, then area of the triangle is

A

1

B

2

C

`sqrt3//2`

D

`sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`(cosA)/a=(cosB)/b=(cosC)/c`
`rArr(cosA)/(ksinA)=(cosB)/(ksinB)=(cosC)/(ksinC)`
`rArrcot A =cot B =cot C`
`rArrA= B = C = 60° rArr Delta ABC` is equilateral
`thereforeDelta=(sqrt3)/4a^(2)=sqrt3`
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