To simplify this expression, we can use the trigonometric identities:

Using these identities, we can find the values of cos(pi/12) and sin(pi/6) as well as cos(pi/6):

cos(pi/12) = √(2+√3)/2
sin(pi/6) = 1/2
cos(pi/6) = √3/2

Now, substitute these values into the expression:

cos(pi/12) cos(pi/12) - sin(pi/6) cos(pi/6)
= (√(2+√3)/2) (√(2+√3)/2) - (1/2) (√3/2)
= (2+√3)/4 - √3/4
= (2+√3 - √3)/4
= 2/4
= 1/2

Therefore, the simplified expression is 1/2.