Question

=>Expert Answers Required
If angle A and angle B are acute angles such that cos A=cosB, then show that angle A=angle B.​

Answer 1

Given,

∠A  and ∠B  are acute angles  ΔABC as  shown in picture,

Now,

in ΔADC

CosA = AD/AC

in ΔBDC

CosB = AD/BC

Given,

CosA = CosB

AD/AC = AD/BC

AC  = BC

We know that, in  a triangle if  two opposite sides are euqal, there corresponding angles  will be  also equal. Hence,

∠A = ∠B