Question

If angle A and angle B are acute angles such that cosA= cos B . Show that angleA = angle B​

Answer 1

Answer:

According to the question:-

Let cos A= Hypotenuse / side adjacent A

​        =  AB / AC

Similarly,

cos B= Hypotenuse / side adjacent B

        = AB / BC

Given that:

cos A=cos B

AB / AC  = AB / BC

​AC=BC

In triangle,

Since, Angles opposite equal side are equal

Therefore,

∠B=∠A

Answer 2

Answer:

cos A = B1/H cos B = B2/H. here B1,B2 represent base and H represent hypotenuse. cos A = cos B. hence, B1= B2 therefore, angle A = angle B because angle opposite to equal sides are equal. here B1 is side AC and B2 is side AB and angle C is right angle