已知cos(a-π/6)+sina=(4*根号3)/5,则sin(a+7π/6)的值是( )
问题描述：
已知cos(a-π/6)+sina=(4*根号3)/5,则sin(a+7π/6)的值是( )
答
cos(a-π/6)+sina=4√3/5展开cosacosπ/6+sinasinπ/6+sina=4√3/5√3/2*cosa+3/2*sina=4√3/51/2*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