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