已知cos(A-π/6)+sinA=4/5倍根号3.求sin(A+7π/6)的值.

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已知cos(A-π/6)+sinA=4/5倍根号3.求sin(A+7π/6)的值.
已知cos(A-π/6)+sinA=4/5倍根号3.求sin(A+7π/6)的值.

已知cos(A-π/6)+sinA=4/5倍根号3.求sin(A+7π/6)的值.
cos(A-π/6)+sinA=4√3/5
cosAcosπ/6+sinAsinπ/6+sinA=4√3/5
cosAcosπ/6+sinA*1/2+sinA=4√3/5
√3/2cosA+3/2sinA=4√3/5
√3(1/2cosA+√3/2sinA)=4√3/5
√3(sinπ/6cosA+cosπ/6sinA)=4√3/5
√3sin(π/6+A)=4√3/5
sin(π/6+A)=4/5
sin(A+7π/6)
=sin(π+A+π/6)
=-sin(π/6+A)
=-4/5