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

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

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best_answer

We have, A and B are two acute angles of triangle ABC and \cos A =\cos B


According to question,
In triangle ABC,
\cos A =\cos B
 \frac{AC}{AB}=\frac{BC}{AB}
\Rightarrow AC = AB
Therefore, \angleA = \angle B   [angle opposite to equal sides are equal]

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