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Conditional Identities

If 2 sin C co...

Question

If $2 sin C cos A = sin B,$ then $△ A B C$ is

Isosceles triangle

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equilateral triangle

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right angle triangle

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none of the options

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Solution

The correct option is A Isosceles triangle
$2 sin C cos A = sin B \Rightarrow sin (C + A) + sin (C - A) = sin B$
We know that,
$A + B + C = π$
$\Rightarrow sin B + sin (C - A) = sin B \Rightarrow sin (C - A) = 0 \Rightarrow C = A$

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