[tex]cos(\pi-\dfrac{\pi}{12})=-\cos\dfrac{\pi}{12}=-\cos(\dfrac{\pi}{3}-\dfrac{\pi}{4})=-\cos\dfrac{\pi}{3}cos\dfrac{\pi}{4}-sin\dfrac{\pi}{3}sin\dfrac{\pi}{4}=[/tex]
[tex]=-\dfrac12\cdot\dfrac{\sqrt2}{2}-\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}=-\dfrac{\sqrt2}{4}(1+\sqrt3)[/tex]
