If the middle term of $(\large\frac{1}{x}$$+x\sin x)^{10}$ is equal to $7\large\frac{7}{8}$ then value of $x$ is

Question

$\begin{array}{1 1}(A)\;2n\pi+\large\frac{\pi}{6}\\(B)\;n\pi+\large\frac{\pi}{6}\\(C)\;n\pi+(-1)^n\large\frac{\pi}{6}\\(D)\;n\pi+(-1)^n\large\frac{\pi}{3}\end{array} $