In a right angled triangle ABC,
cos A = \(\frac{AC}{AB}\) and cos B = \(\frac{BC}{AB}\)
∵ cos A = cos B
\(\frac{AC}{AB}\) = \(\frac{BC}{AB}\)
∴ AC = BC
We have, opposite sides of equal angles are equal.
Therefore, In a right angled triangle ABC
∠A = ∠B = 45°