Question

If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

Answer 1

cos A = \(\frac{AC}{AB}\) and cos B = \(\frac{BC}{AB}\)

∵ cos A = cos B

\(\frac{AC}{AB} = \frac{BC}{AB}\)

\(\therefore\) AC = BC

We have, opposite sides of equal angles are equal. Therefore, In a right angled triangle ABC

∠A = ∠B = 45°