Question

If angleA and angleB are acute angles such that cosA=cosB then show that angleA=angleB

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Answer 1

Given:-

∠A and ∠B are acute ∠'s.

cos A = cos B

To show:-

∠A = ∠B

Solution:-

Since, cos A = cos B:

$\tt\large\frac{AC}{AB} = \frac{BC}{AB}$

$\large \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt\boxed{AC = BC}$

∴∠A = ∠B (∠'s opposite to equal sides are equal in isosceles ∆)

$\tt\huge\red {Proved!}$