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

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

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

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