Question

If angle A and angle B are acute angles such that cosA=cosB, then show that angle A=angle B

Answer 1

If the angle A and B are acute angles such that cosA = cosB.

We have to show ∠A = ∠B

Let ABC is a right angled triangle where C is right angle.

∴ AB is hypotenuse of ABC.

We know, cosine = base/hypotenuse.

For cosA, BC is taken as base and for cosB, AC is taken as Base.

Now, cosA = BC/AB , and cosB = AC/AB

Given, cosA = cosB

⇒ BC/AB = AC/AB

⇒ BC = AC

We know, if two sides of a triangle are same, the two angles opposite to the equal sides must be equal.

∴ ∠A = ∠B

hence proved//.

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Answer 2

Answer:

Super abhi sir you need to help all