The range of both sin(t) and cos(t) is [-1, 1], meaning the largest either get is 1 and the smallest either get is -1.
That means that sin(t) - cos(t) can only be 1 if sin(t) = 1 at the same time that cos(t) = 0 ( 1 - 0 = 1) or when sin(t) = 0 at the same time that cos(t) = -1 (0 - -1 = 1).
Case 1. sin(t) = 1 AND cos(t) = 0
This only occurs at π/2
Case 2 sin(t) = 0 AND cos(t) = -1
This only occurs at π
However, the problem gives no restriction to the domain. That means that we need to include both those values and also every 2π increment. So the answer is:
t = π/2 + 2πk and t = π + 2πk where k is any integer