f(x)=sin(2x+π/6)+sin(2x -π/6)+2cos²x
=2sin2xcosπ/6+1-cos2x
=根号3sin2x-cos2x+1
=2sin(2x-π/6)+1
(1),T=2π/2=π
(2),f(x)max=3
sin(2x-π/6)=1
2x-π/6=2kπ+π/2
x-π/12=kπ+π/4
x=kπ+π/3 (k∈Z)
f(x)=sin(2x+π/6)+sin(2x -π/6)+2cos²x
=2sin2xcosπ/6+1-cos2x
=根号3sin2x-cos2x+1
=2sin(2x-π/6)+1
(1),T=2π/2=π
(2),f(x)max=3
sin(2x-π/6)=1
2x-π/6=2kπ+π/2
x-π/12=kπ+π/4
x=kπ+π/3 (k∈Z)