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

Solution:

Given:

$\cos A=\cos B$.....(1)

To show: $\angle A=\angle B$

$\triangle A B C$ is as shown in figure below

Therefore

$\frac{A C}{A B}=\frac{B C}{A B}$

Now observe that denominator of above equality is same that is AB

Hence $\frac{A C}{A B}=\frac{B C}{A B}$ only when $A C=B C$

Therefore $A C=B C$.....(2)

We know that when two sides of a triangle are equal, then angle opposite to the sides are also equal.

Therefore from equation (2)

We can say that

Angle opposite to side AC = Angle opposite to side BC

Therefore,

$\angle B=\angle A$

Hence, $\angle A=\angle B$