Question

In this triangle, cos A/cos B = ___

Answer 1

arccos(3/4.24) = 44.96° or 45°

This is for angles A and B

Answer 2

cos Ф = (adjacent side) / (hypotenuse)

cos A = 3/4.24 = 0.707
cos B = 3/4.24 = 0.707
cos (A) / COS B) = 0.707/0.707 = 1

2ND METHODE (trigonometric solution. I don't know what is your level)
The triangle is right isosceles and ∠ A = ∠ B = 45°
cos A = cos 45° = (√2)/2
cos B = cos 45° = (√2)/2
cos A / cos B = 1