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In a triangle ABC, if cos A = (sin B)/(2sin C), then which of the following is true?

1. a = b = c
2. c = a
3. a = b
4. b = c

Correct answer: c = a

Solution

The equation ( rac{ ext{sin} B}{2 ext{sin} C} = ext{cos} A) implies a specific relationship between the angles and sides of triangle ABC, leading to the conclusion that sides a and c must be equal, thus confirming that c = a.

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