Question

If ∠A and ∠B are two acute angles of two triangles such that cos A = cos B then show that ∠A = ∠B

Answer 1

We have, cos A = cos B
         so, Sin (90-A) = Sin (90-B)         [∵Sin (90-x ) = Cos x and vice-versa]
             So, 90-A = 90-B
                   so, -B+A = 0
                       Hence, A = B.

Answer 2

Here is ur ans
Take a right angled triangle ABC roght angled at C ;

Here, cos A = AC/AB

cos B = BC/AB

Given cos A = Cos B;

AC/AB = BC/AB

So,angle A =angle B
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