Question

if angle a and angle b are acute angles such that cos A=cosB , then show that angle A = angle B​

Answer 1

Given cosA= cosB,

consider a triangle abc right angled at C, such that AB is hypotenuse, BC is base and AC is perpendicular

COS A= AC/AB--------------------1

COS B= BC/AB--------------------2

Upon equating 1 with 2,

AC/AB = BC/AB

                         ....... AB gets cancelled

AC=BC( opposite angles of equal sides are equal)

therefore ANGLE <A= ANGLE <B

hope it helps you :)