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Q6. 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

=> \( \frac{AC}{AB} \ = \ \frac{BC}{AB} \)
=> \( AC \ = \ BC \)

∴ \( ∠ \ A \ = \ ∠ \ B \) [∵ Angles opposite to equal sides are equal]