We can use the following identities to simplify the expression:

• arccos(-x) = pi - arccos(x) for x between -1 and 1
• arcsin(-x) = -arcsin(x) for x between -1 and 1

First, we can find the value of arccos(-0.5) using the fact that cos(arccos(x)) = x for x between -1 and 1. Therefore, we have:

cos(arccos(-0.5)) = -0.5

Using the inverse cosine function, we find that arccos(-0.5) = 2*pi/3.

Next, we can find the value of arcsin(-0.5) using the fact that sin(arcsin(x)) = x for x between -1 and 1. Therefore, we have:

sin(arcsin(-0.5)) = -0.5

Using the inverse sine function, we find that arcsin(-0.5) = -pi/6.

Finally, we can substitute these values into the original expression:

arccos(-0.5) + arcsin(-0.5) = 2pi/3 - pi/6 = (4pi)/6 - pi/6 = (3*pi)/6 = pi/2

Therefore, arccos(-0.5) + arcsin(-0.5) = pi/2.