if cosα = sinβ and 0° ≤ β ≤ 90°, usually it means is a right-triangle, so there's another angle that is not α or β that is 90°, and in which case angles α and β are "complementary angles", namely α + β = 90°, like in the example in the picture below.
what the dickens does all that mean? well, it means that if α = 26.4°, then
α + β = 90°
26.4° + β = 90°
β = 90° - 26.4°.
