# Math Help - If b\cos{\beta} = c\cos{\gamma} prove that

1. ## If b\cos{\beta} = c\cos{\gamma} prove that

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

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

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

2. Originally Posted by bigwave
If $b\cos{\beta} = c\cos{\gamma}$

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

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
$
A,\beta,\gamma$
are the corresponding angles
Sine rule: $\frac b{\sin \beta} = \frac c{\sin\gamma}$. Deduce that $\sin\beta\cos\beta = \sin\gamma\cos\gamma$, hence $\sin2\beta = \sin2\gamma$. If two angles have the same sine then they are either equal or supplementary.