If $\int \large\frac{\sin ^8 x -\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x}$$dx=A \sin 2x+B,$ then $A=$

Question

$$\begin {array} {1 1} (a)\;-\frac{1}{2} & \quad (b)\;-1 \\ (c)\;\frac{1}{2} & \quad (d)\;1 \end {array}$$