求sin(2nπ+2π/3)+cos（nπ+4π/3）的值,n属于Z

求sin(2nπ+2π/3)+cos（nπ+4π/3）的值,n属于Z
求sin(2nπ+2π/3)+cos（nπ+4π/3）的值,n属于Z

求sin(2nπ+2π/3)+cos（nπ+4π/3）的值,n属于Z
1)当n为偶数时,sin(2nπ+2π/3)+cos(nπ+4π/3)=sin2π/3+cos4π/3)
=sin(π-π/3)+cos(π+π/3).
=sinπ/3-cosπ/3
=sinπ/3-cosπ/3.
=√3/2-1/2
2）当n为奇数时,sin(2nπ+2π/3)+cos(nπ+4π/3)=sin2π/3-cos4π/3.
=√3/2-(-1/2).
=√3/2+1/2.

sin(2nπ+2π/3)+cos（nπ+4π/3）
=sin(2π/3)+cos((n+1)π+π/3)
=sin(π/3)+cos((n+1)π+π/3)
当n是奇数时，原式=sin(π/3)+cos(π/3)=(（根号3）/2)+1/2=(1+根号3）/2
当n是偶数时，原式=sin(π/3)+cos((n+1)π+π/3)=sin(π/3)-cos(π/3）=)=(（根号3）/2)-1/2