If $cos A = sin B / (2 sin C)$ , prove that $△ A B C$ is isosceles.

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Solution

Since $cos A = \frac{sin B}{2 sin C}$ , we have
$\frac{b^{2} + c^{2} - a^{2}}{2 a b} = \frac{b}{2 c}$
or $b^{2} + c^{2} - a^{2} = b^{2}$ or $c^{2} = a^{2}$ .
Hence $c = a$ and so the $△ A B C$ is isosceles.

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