已知函数f(x)=2cos(x+π/3)[sin(x+π/3)-更号3倍的cos(x+π/3)]求f(x)的值域和最小正周期

已知函数f(x)=2cos(x+π/3)[sin(x+π/3)-更号3倍的cos(x+π/3)]求f(x)的值域和最小正周期
已知函数f(x)=2cos(x+π/3)[sin(x+π/3)-更号3倍的cos(x+π/3)]求f(x)的值域和最小正周期

已知函数f(x)=2cos(x+π/3)[sin(x+π/3)-更号3倍的cos(x+π/3)]求f(x)的值域和最小正周期
f(x)=2cos(x+π/3)[sin(x+π/3)-√3cos(x+π/3)]
=4cos(x+π/3)[1/2 sin(x+π/3)-√3/2 cos(x+π/3)]
=4cos(x+π/3)sin(x+π/3+π/3)
=4cos(x+π/3)sin(x+2π/3)
=4×(1/2)×[sin(x+2π/3+x+π/3)+sin(x+2π/3-x-π/3)]
=2×[sin(2x+π)+sin(π/3)]
=2×[sin(2x+π)+√3/2]
=-2sin(2x)+√3
值域[√3-2,√3+2]
w=π