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

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Answer 1 · 2018-03-10T06:16:10

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

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