f(x)=sin(2x+π/6)+sin(2x-π/6)+cos(2x)+a
=sin(2x)cos(π/6)+cos(2x)sin(π/6)+sin(2x)cos(π/6)-cos(2x)sin(π/6)+cos(2x)+a
=2sin(2x)cos(π/6)+cos(2x)+a
=√3sin(2x)+cos(2x)+a
=2sin(2x+π/6)+a
f(x)的最小正周期为π
f(x)=sin(2x+π/6)+sin(2x-π/6)+cos(2x)+a
=sin(2x)cos(π/6)+cos(2x)sin(π/6)+sin(2x)cos(π/6)-cos(2x)sin(π/6)+cos(2x)+a
=2sin(2x)cos(π/6)+cos(2x)+a
=√3sin(2x)+cos(2x)+a
=2sin(2x+π/6)+a
f(x)的最小正周期为π