Question

How do you prove `\frac{a-c}{c} = \frac{\sin A - \sin C}{\sin C}` using the law of sines?

Answer 1

According to Lami's theorem,we know,

`a/sin A =b/sin B =c/sin C=R`

so, `a=R sin A,b=R sin B` & `c=R sin C`

So, `(a-c)/c=(R sin A - R sin C)/(R sin C)=(R( sin A - sin C))/(R sin C)=(sin A - sin C)/sin C`