已知sin(a+π/3)+sina=-4√3/5,-π/2

sinacosπ/3+cosasinπ/3+sina=-4√3/5sina*3/2+cosa*√3/2=-4√3/5√3(sina*√3/2+cpsa*1/2)=-4√3/5sinasinπ/3+cpsacosπ/3=-4/5cos(π/3-a)=-4/5则cos(a+2π/3)=-cos[π-(a+2π/3)]=-cos(π/3-a)=4/5