Question

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

Answer 1

Consider a right angled ΔACB

According to the question, Cos A = Cos B.

Therefore, by diagram we get:

→ Cos A = BC/AB

→ Cos B = AC/AB

Therefore equating the RHS of both we get:

→ BC/AB = AC/AB

Cancelling the denominators on both sides we get:

→ BC = AC

Therefore sides BC and AC are equal.

We know the property that, angles opposite to equal sides are equal.

Hence Angle opposite to BC is A and Angle opposite to AC is B.

Therefore Angle A = Angle B.

Answer 2

Answer:

directly removing cos on both sides ,u can get