Question

If ∠A and ∠B are acute angles such that tan A = tan B, the prove that ∠A=∠B.

Answer 1

Consider ΔABC to be a right angled triangle.

angle C = 90 degree

tan A = BC/AC and

tan B = AC/BC

Given: tan A = tan B

So, BC/AC = AC/BC

BC² = AC²

BC = AC

Which implies, ∠ A = ∠ B (using triangle opposite and equal angles property)