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

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

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

Solution:

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

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

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

$\Rightarrow c^{2}=a^{2}$

$\Rightarrow c=a$