If $\displaystyle b\cos{\beta} = c\cos{\gamma}$

prove that either $\displaystyle b=c$ or $\displaystyle A=90^o$

tried for an hour trying to prove this with the law of cosines but that didn't seem to go anywhere

a,b,c are the sides of any triangle

$\displaystyle

A,\beta,\gamma$ are the corresponding angles