$\frac{{\mathrm{Sin}}^3{43}^0-{\mathrm{Sin}}^3{17}^0}{\mathrm{Sin}{43}^0-\mathrm{Sin}{17}^0}=$

$$\begin{gathered} \frac{{\mathrm{Sin}}^3{43}^0-{\mathrm{Sin}}^3{17}^0}{\mathrm{Sin}{43}^0-\mathrm{Sin}{17}^0} \\ =\frac{\left(\mathrm{Sin}{43}^0-\mathrm{Sin}{17}^0\right)\left({\mathrm{Sin}}^2{43}^0+\mathrm{Sin}{43}^0\mathrm{Sin}{17}^0+{\mathrm{Sin}}^2{17}^0\right)}{\mathrm{Sin}{43}^0-\mathrm{Sin}{17}^0} \\ ={\mathrm{Sin}}^2{43}^0+\mathrm{Sin}{43}^0\mathrm{Sin}{17}^0+{\mathrm{Sin}}^2{17}^0 \\ =1-({\cos }^2{43}^o-{\sin }^2{17}^o)+\frac{1}{2}2\mathrm{Sin}{43}^0\mathrm{Sin}{17}^0 \\ =1-\cos {60}^o\cos {26}^o+\frac{1}{2}(\cos {26}^o-\cos {60}^o) \\ =1-\frac{1}{2}c\mathrm{os}{26}^o+\frac{1}{2}c\mathrm{os}{26}^o-\frac{1}{4} \\ =\frac{3}{4} \end{gathered}$$