Question

Answer each of the following questions in one word or one sentence or as per exact requirement of the question.

In a ∆ABC, if $\cos A=\frac{\sin B}{2\sin C}$, then show that c = a.

Answer 1

Given: $\cos A=\frac{\sin B}{2\sin C}$

$\Rightarrow \frac{b^2+c^2-a^2}{2bc}=\frac{b}{2c}$ (Using sine rule and cosine rule)

$\Rightarrow b^2+c^2-a^2=b^2$

$\Rightarrow c^2=a^2$

$\Rightarrow c=a$