Let's use the difference of squares formula to simplify this expression:

(cos(π/12) - sin(π/12)) * (cos(π/12) + sin(π/12))
= cos^2(π/12) - sin^2(π/12)
= cos^2(π/12) - (1 - cos^2(π/12))
= cos^2(π/12) - 1 + cos^2(π/12)
= 2cos^2(π/12) - 1

Therefore, the simplified expression is 2cos^2(π/12) - 1.