Докажи тождество

\({\dfrac{\sqrt{2}\cos\alpha-2\cos\left(\dfrac{\pi}{4}-\alpha\right)}{2\sin\left(\dfrac{\pi}{6}+\alpha\right)-\sqrt{3}\sin\alpha}\raisebox{-2.5em}{\),\(}\mathrlap{\,=}}\) \({=-\sqrt{2}\tg\alpha}\) .