If tan(α) = 512512 and sin(β) = 3535, where α and β are acute angles, calculate the value of tan(α - β).

To solve this problem, we can use the formula for the tangent of the difference of two angles, which is:

tan(α - β) = (tan(α) - tan(β)) / (1 + tan(α)tan(β))

Given that tan(α) = 512/512 = 1 and sin(β) = 35/35 = 1, we can find the value of tan(β) using the Pythagorean identity sin²(β) + cos²(β) = 1. Since sin(β) = 1, we have cos(β) = sqrt(1 - sin²(β)) = sqrt(1 - 1) = 0. Therefore, tan(β) = sin(β) / cos(β) = 1 / 0, which is undefined.

However, in this case, since both tan(α) and sin(β) are equal to 1, the angles α and β are both equal to 45 degrees (or π/4 radians). Therefore, α - β = 45 - 45 = 0, and tan(0) = 0.

So, tan(α - β) = 0.