Let's first find the values of arcsin(-1/2) and arcsin(1).

arcsin(-1/2) is the angle whose sine is -1/2. Since the sine of -30 degrees is -1/2, we have arcsin(-1/2) = -30 degrees.

arcsin(1) is the angle whose sine is 1. Since the sine of 90 degrees is 1, we have arcsin(1) = 90 degrees.

Now, we can substitute these values into the given expression:

cos(arcsin(-1/2) - arcsin(1)) = cos(-30 - 90)

Since the cosine function is periodic with a period of 360 degrees, we can add 360 degrees to -30 degrees to find an equivalent angle within the interval [-180, 180] degrees:

cos(-30 - 90) = cos(-120) = cos(240)

Now, 240 degrees is in the second quadrant, where the cosine function is negative. The reference angle for 240 degrees is 180 degrees. Thus, we have:

cos(240) = -cos(180) = -(-1) = 1

Therefore, cos(arcsin(-1/2) - arcsin(1)) = 1.