$A= cos\frac{\pi}{3}.cosx - sin\frac{\pi}{3}.sinx - sin\frac{\pi}{6}.cosx-cos\frac{\pi}{6}.sinx$
$= \frac{1}{2}cosx-\frac{\sqrt3}{2}sinx - \frac{1}{2}cosx-\frac{\sqrt3}{2}sinx$
$=0$
$B=sin(6\pi-\frac{\pi}{12}).cos(\frac{\pi}{2}-\frac{\pi}{12})$
$= -sin\frac{\pi}{12}.sin\frac{\pi}{12}$
$=-sin^2(\frac{\pi}{3}+\frac{\pi}{4})$
$= -(sin\frac{\pi}{3}cos\frac{\pi}{4}+cos\frac{\pi}{3}.sin\frac{\pi}{4})^2$
$= \frac{-2-\sqrt3}{4}$
