Question

If $\frac{sin(x+y)}{sin(x-y)}=\frac{a+b}{a-b},$ Show that $\frac{tanx}{tany}=\frac{a}{b}.$

Answer 1

$\frac{sin(x+y)}{sin(x-y)}=\frac{a+b}{a-b}$
$\Rightarrow \frac{sinx.cosy+siny.cosx+sinx.cosy-siny.cosx}{sinx.cosy+siny.cosx-sinx.cosy+siny.cosx}=\frac{a+b+a-b}{a+b-a+b}$
$\Rightarrow \frac{2sinx.cosy}{2siny.cosx}=\frac{2a}{2b}\Rightarrow \frac{tanx}{tany}=\frac{a}{b}$
Hence proved.