f(X)=2sin（X+π/3）-2sinX
=2sinX cos(π/3）+2cosX sin(π/3）-2sinX
=sinX+√3cosX-2sinX
=√3cosX-sinX
=2*[(√3/2)cosX-(1/2)sinX]
=2*[sin(π/3)cosX-cos(π/3）sinX]
=2sin(π/3-X)由此 就解出f(X)
（1）cosX=√3/3,又X属于[-π/2,0],则sinX=-√6/3
由f(X)=√3cosX-sinX=1+√6/3
（2）f(X)=2sin(π/3-X),X属于[-π/2,0],
则π/3-X属于[π/3,5π/6]
画个图便知f(X)的值域为[1,2]