[tex]\dfrac{\sin 70+\cos 80}{\cos 10-\sin 20} = \dfrac{\sin(90-20)+\cos 80}{\cos(90-80)-\sin 20} = \dfrac{\cos 20+\cos 80}{\sin 80-\sin 20} = \\ \\ =\dfrac{2\cos\dfrac{80+20}{2}\cos\dfrac{80-20}{2}}{2\cos\dfrac{80+20}{2}\sin\dfrac{80-20}{2}} = \dfrac{\cos 50\cos 30}{\cos 50\sin 30} = \dfrac{\cos 30}{\sin 30} = \dfrac{\dfrac{\sqrt 3}{2}}{\dfrac{1}{2}} = \boxed{\sqrt 3}[/tex]
