Multiple choice general knowledge math & puzzles

In a triangle ABC if cos B = sin A / 2 sin C then the triangle is

  1. isosceles

  2. equilateral

  3. right angled

  4. none
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A Correct answer
Explanation

Using the Sine Rule (a/sinA = b/sinB = c/sinC), we substitute sinA = ka and sinC = kc. The equation becomes cos B = ka / 2kc = a / 2c. By the Law of Cosines, cos B = (a^2 + c^2 - b^2) / 2ac. Setting them equal: a/2c = (a^2 + c^2 - b^2) / 2ac leads to a^2 = a^2 + c^2 - b^2, so b=c, making it isosceles.

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