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Question
Answer 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.
Solution
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)
\[\Rightarrow b^2 + c^2 - a^2 = b^2\]
\[\Rightarrow c^2 = a^2\]
\[\Rightarrow c = a\]
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