已知函数f(χ)=sin(2x+π/6 )+sin(2x- π/6)+cos2x+1(x∈R),

f(x)=(√3/2)sin2x+(1/2)cos2x+(√3/2)sin2x-(1/2)cos2x+cos2x+1
=√3sin2x+cos2x+1
=2sin(2x+π/6)+1
周期T=2π/2=π
对称轴：2x+π/6=π/2+kπ,得对称轴为：x=-π/6+kπ/2,k∈Z
对称中心：2x+π/6=kπ,得对称中心为：（-π/12+kπ/2,0）,k∈Z
单调增区间：
-π/2+2kπ