已知cos(a-π/6）+sina=4根号下3/5,则sin(a+7π/6)=?

根据:cos（a-π/6）+sina=（4*根号3）/5
有:cosacosπ/6+sinasinπ/6+sina=（4*根号3）/5
(根号3)/2cosa+3/2sina=（4*根号3）/5
得到:cosa+(根号3)sina=8/5
所以:
sin（a+7π/6）=sinacos7π/6+cosasin7π/6=(-根号3)/2sina-1/2cosa
=(-1/2)(cosa+根号3sina)
=(-1/2)*8/5
=-4/5