Question

In a triangle ABC, if $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$, then $△ABC$ is

• A. Right-angled
• B. Isosceles right-angled
• C. Equilateral
• D. Scalene

Answer 1

The correct option is C Equilateral

It is given that $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$

Sine rule tells us that, $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}=\frac{1}{2R}$

$\Rightarrow \frac{\cos A}{2R\sin A}=\frac{\cos B}{2R\sin B}=\frac{\cos C}{2R\sin C}$

$\therefore \tan A=\tan B=\tan C$

Implying that, the triangle is equilateral.