$\displaystyle{\frac{1}{(2sin10^{\circ})}-2sin70^{\circ} = \frac{1}{(2sin10^{\circ})}-2sin(90^{\circ}-20^{\circ}) = \frac{1}{(2sin10^{\circ})}-2cos20^{\circ}}$
$\displaystyle{= \frac{1-4cos20^{\circ}sin10^{\circ}}{2sin10^{\circ}} = \frac{1-2(2cos20^{\circ}sin10^{\circ})}{(2sin10^{\circ})}}$
$\displaystyle{= \frac{1}{2sin10^{\circ}}[1-2\{sin(20^{\circ}+10^{\circ})-sin(20^{\circ}-10^{\circ})\}]}$
$= \displaystyle{\frac{1}{2sin10^{\circ}}[1-2{sin30^{\circ}+2sin10^{\circ}}] = \frac{1}{2sin10^{\circ}}[1-2\frac{1}{2}+2sin10^{\circ}]}$
$= \displaystyle{\frac{1}{2sin10^{\circ}}[1-1+2sin10^{\circ}] = \frac{1}{2sin10^{\circ}}[2sin10^{\circ}] =1}$