$$\begin{gathered} \text{ Statement-I : }\cos {52}^0+\cos {68}^0+\cos {172}^{\circ }=\frac{1}{2} \\ \text{ Statement-II: }4\sin A{\cos }^{3}A-4\cos A{\sin }^{3}A=\cos 4A \\ \text{ Which of the above statements is correct? } \end{gathered}$$

$$\begin{gathered} \cos {52}^0+\cos {68}^0+\cos {172}^{\circ } \\ =\left(\cos {68}^0+\cos {52}^0\right)+\cos \left(\mathrm{\pi }-8°\right) \\ =2\cos \frac{{68}^0+{52}^0}{2}\cos \frac{{68}^0-{52}^0}{2}-\cos 8° \\ =2\cos 60°\cos 8°-\cos 8°=0 \end{gathered}$$

$$\begin{gathered} \text{ Statement-II: }4\sin A{\cos }^{3}A-4\cos A{\sin }^{3}A \\ =4\sin AcosA\left({\cos }^{2}A-{\sin }^{2}A\right) \\ =2\sin 2A\cos 2A \\ =\sin 4A \end{gathered}$$

$\text{ Neither I nor II }$