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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
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Verified Answer
The correct answer is:
an equilateral triangle
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.
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.
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