Question

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

Answer 1

∠A and ∠B are acute angles

Cos A = cos B S.T ∠A = ∠B

Let us consider right angled triangle ACB.

We have `cos A = "adjacent side"/"Hypotenuse"`

`= (AC)/(AB)`

`cos B = (BC)/(AB)`

cos A = cos B

`(AC)/(AB) = (BC)/(AB)`

AC = BC

∠A = ∠B