Question

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

Answer 1

$\frac{\cos A}{a}=\frac{\cos B}{b},$ ....(i)
$\frac{\sin A}{a}=\frac{\sin B}{b}$ .........(ii) (True for any triangle)
Hence $\frac{\left(2\right)}{\left(1\right)}$
$\tan A=\tan B$
$A=B$
So , $\Delta ABC$ is isosceles as two angles are equal.