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In a triangle ABC, if (cosA)/a=(cosB)/b=...

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

Text Solution

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The correct Answer is:
`sqrt3` sq. unit
`(cos A)/(a) = (cos B)/(b) = (cos C)/(c)`
or `(cos A)/(2R sin A) = (cos B)/(2R sin B) = (cos C)/(2R sin C)`
or `tan A = tan B = tan C`
Hence, triangle is equilateral.
Therefore, Area of triangle `= (sqrt3)/(4) a^(2) = sqrt3` (as a = 2)
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