Question

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

Answer 1

Given:

…… (1)

To show:

is as shown in figure below

Now since ……from (1)

Therefore

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

Hence only when

Therefore …… (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,

Hence,