Question

If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

Answer 1

SOLUTION :  

GIVEN : cos A = cos B  

Draw  right ∆ABC, ∠C = 90°.  

With reference to ∠A , base = AC, Hypotenuse = AB , perpendicular = BC

With reference to ∠B , base = BC, Hypotenuse = AB perpendicular = AC

cos A = cos B  (Given)

Base/ Hypotenuse (AC/AB) = Base/ Hypotenuse (BC/AB)

AC/AB = BC/AB

AC = BC  

∠B = ∠A

[In a triangle angles opposite to equal sides are also equal]

Hence proved .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

hello...




∠A  and ∠B  are acute angles  ΔABC


in ΔADC


CosA = AD/AC


in ΔBDC


CosB = AD/BC

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.

so.......


∠A = ∠B

thank you...