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

$cos(\pi /12)-sin(\pi /12)$ * $cos(\pi /12)+sin(\pi /12)$ = cos^2$\pi /12$ - sin^2$\pi /12$ = cos^2$\pi /12$ - $1-co{s}^2(\pi /12)$ = cos^2$\pi /12$ - 1 + cos^2$\pi /12$ = 2cos^2$\pi /12$ - 1

Therefore, the simplified expression is 2cos^2$\pi /12$ - 1.