Q6. If $$∠\ A$$ and $$∠\ B$$ are acute angles such that cos A = cos B, then show that $$∠ \ A \ = \ ∠ \ B$$.

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]