In $\triangle A B C$, if $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos c}{c}$ with usual notations, then the…
In $\triangle A B C$, if $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos c}{c}$ with usual notations, then the triangle is
- an isosceles triangle
- an equilateral triangle
- a right angled scalene triangle
- a scalene triangle
Solution
From sine rule $a / \sin A=b / \sin B=c / \sin C=2 R$
Given situation
$a / \cos A=b / \cos B=c / \cos B=k$
$2 R \sin A=k \cos A$
$\tan A=\tan B=\tan C$
Hence it is equilateral triangle.
Asked in: MHT CET 2020 (14 Oct Shift 2)
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