If $\sin x+\cos x=a$ then $\sin ^6x+\cos ^6x$=_______

Question

$\begin{array}{1 1}(A)\;\large\frac{1}{4}\normalsize [4-3(a^2-1)^2]&(B)\;\large\frac{1}{2}\normalsize [2-3(a^2-1)^2]\\(C)\;a^2&(D)\;2a^6\end{array} $