Question

if angle a and angle b are acute angles such that cos A =cosB, then show that angleA =angleB.

Answer 1

suppose a triangle ACB right angled at C then Cos A= side adjacent <A / Hypotenuse
=AC/AB
CosB= side adjacent <B/ Hypotenuse
= BC/AB
It is given that Cos A= Cos B
so AC/AB=BC/AB
hence <A=<B

Answer 2

In triangle ACB right angled at C
If cos A = cos B
AC/AB = BC/AB
So AC = BC