阅读下面这首诗。
                                                                                                                                       秋夜山居
                                                                                                                                       唐•施肩吾
                                                                                                                去雁声遥人语绝，谁家素机①织新雪。
                                                                                                                 秋山野客②醉醒时，百尺老松衔半月。
       【注释】①素机：织布机。②野客：离乡在外的游客。

若α∈$\left(0,\frac{\mathrm{\pi }}{2}\right)$，且$\cos \left(\alpha +\frac{\mathrm{\pi }}{6}\right)=-\frac{\sqrt{2}}{4}$，则cosα=____ 

下列诗句，哪一项是正确的（《中国诗词大会》第二季第二期）（    ）