Question

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

Answer 1

In ABC

cosB=B/H=BC/AB & cosA=B/H=AC/AB

Also, cosA= cosB (Given)

= AC/AB = BC/AB

= AC = BC

= angleA = angleB ( since angles opposite to equal sides are equal.)

Answer 2

SOLUTION

It is given that angle A & angle B are acute angles,

then angle C= 90°

Also,

CosA = cosB (given)

=) AC/AB= BC/AB

=) AC= BC

Since, angles opposite to equal sides are equal, therefore angle A = angle B.

hope it helps ✔️