Question

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

Answer 1

cos(a-π/6)+sina=4√3/5

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cosacosπ/6+sinasinπ/6+sina=4√3/5

√3/2*cosa+3/2*sina=4√3/5

1/2*cosa+√3/2*sina=4/5

∴sin(a+π/6)=4/5

∴sin(a+7π/6)=sin(π+π/6)

=-sin(a+π/6)=-4/5