First, we need to find the value of each individual term:

Let's find the value of arcsin(1/2). This means finding the angle whose sine is 1/2. The sine of π/6 (30 degrees) is 1/2, so arcsin(1/2) = π/6.

Let's find the value of arccos(1). This means finding the angle whose cosine is 1. The cosine of 0 is 1, so arccos(1) = 0.

Now we can substitute these values into the expression:

cos(arcsin(1/2)) - arccos(1)
= cos(π/6) - 0
= cos(π/6)
= √3/2

Therefore, the final answer is √3/2.