Sin 70°cos 10°-cos 70°sin 10=√3/2

Let a = 70° and b = 10° (and a-b=70-10 = 60)

We have the following trigonometric identity:

sin (a-b) = sin (a). cos (b) - sin (b). cos (a) OR:

sin (70-10) = sin70. cos10 - sin10. cos70

But sin (70-10) = sin (60) and we know that sin (60°) = (√3) / 2