Question

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

Answer 1

In right triangle 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.)
Hence, proved.

Answer 2

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Step-by-step explanation:

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In right ∆ ABC,

As both angle A and angle B are acute and only angle C can be 90°.

Since, in trigonometry we consider a right angled triangle

Given, cos A = cos B

=) AC/AB  = CB/AB

=) AC = CB

Therefore,

Angle A = Angle B (Hence Proved)