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

解析：∵cos(a-π/6)+sina=cosacosπ/6+sinasiπ/6+sina=√3/2cosa+3/2sina=√3(1/2cosa+√3/2sina)=√3sin(a+π/6)=4√3/5即sin(a+π/6）=4/5∴sin(a+7π/6)=sin[π+(a+π/6)]=-sin(a+π/6)=-4/5