Question

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

Answer 1

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Solution:

Suppose a triangle ABC, right-angled at C.

Now, we know the trigonometric ratios,

cos A = AC/AB

cos B = BC/AB

Since, it is given,

cos A = cos B

AC/AB = BC/AB

AC = BC

As we know, the angles opposite to the equal sides are equal, by isosceles triangle theorem.

Therefore, ∠A = ∠B

Answer 2

ANSWER:

Step-by-step explanation:

In triangle ABC ,

Cos A = opposite side / hypo.

= AC / AB -1

Cos B = adjacent side / hypo.

= BC / AB -2

We gave cos A = cos B

Thus by 1 and 2,

AC / AB = BC / AB

Thus

AC . AB = BC . AB

AC = BC

thus AC and BC are two sides of triangle ABC

Thus angle A = angle B

( angles opposite to equal sides are equal )

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