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

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

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

已知cos(a-π/6)+sina=4√3/5,则sin(a+7π/6)=?
cos(a-π/6)+sina=cosacosπ/6+sinasinπ/6+sina =(√3/2)cosa+(3/2)sina=4√3/5 ∴(1/2)cosa+(√3/2)sina=4/5 sin(x+7π/6)=sinacos7π/6+sin7π/6cosa =(-√3/2)sina+(-1/2)cosa=-4/5