Question

In $\Delta ABC,$ if $\frac{\cos A}{a}=\frac{\cos B}{b},$ then show that it is an isosceles triangle.

Answer 1

In $△ABC,$

$⟹\frac{\cos A}{a}=\frac{\cos B}{b}$

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

$⟹\cot A=\cot B$

$⟹A=B$

$⟹△ABC$ is an isosceles triangle