$$ \begin{aligned} \frac{1}{2} \csc 10^{\circ} - 2 \sin 70^{\circ} &= \frac{1}{2 \sin 10^{\circ}} - 2 \sin 70^{\circ} \\ &= \frac{1 - 4 \sin 70^{\circ} \sin 10^{\circ}}{2 \sin 10^{\circ}} \\ &= \frac{1 - 2(2 \sin 70^{\circ} \sin 10^{\circ})}{2 \sin 10^{\circ}} \\ &= \frac{1 - 2(\cos 60^{\circ} - \cos 80^{\circ})}{2 \sin 10^{\circ}} \\ &= \frac{1 - 2(\frac{1}{2} - \sin 10^{\circ})}{2 \sin 10^{\circ}} \\ &= \frac{1 - 1 + 2 \sin 10^{\circ}}{2 \sin 10^{\circ}} \\ &= \frac{2 \sin 10^{\circ}}{2 \sin 10^{\circ}} \\ &= 1 \end{aligned} $$