Let's first find the value of arccos(0.8).

arccos(0.8) is the angle whose cosine is 0.8. This angle is approximately 37 degrees or 0.6435 radians.

Now, we need to find cos(2 * 0.6435).

cos(2 * 0.6435) = cos(1.287)

Using the double angle formula: cos(2x) = cos^2(x) - sin^2(x), we can find cos(1.287).

cos^2(0.6435) = 0.8^2 = 0.64

sin^2(0.6435) = 1 - cos^2(0.6435) = 1 - 0.64 = 0.36

cos(1.287) = cos^2(0.6435) - sin^2(0.6435) = 0.64 - 0.36 = 0.28

Therefore, cos(2arccos(0.8)) = 0.28.