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If \(∠\ A\) and \(∠\ B\) are acute angles such that cos A = cos B, then show that \( ∠ \ A \ = \ ∠ \ B \).
Answer :
In \( ∆ \ ABC \),
\( cosA \ = \ \frac{AC}{AB} \ = \ \frac{B}{H} \)
and, \( cosB \ = \ \frac{BC}{AB} \)
But given that, cos A = cos B
=> \( \frac{AC}{AB} \ = \ \frac{BC}{AB} \)
=> \( AC \ = \ BC \)
\(\therefore \) \( ∠ \ A \ = \ ∠ \ B \) [\(\because \) Angles opposite to equal sides are equal]