(1)f(x)=sinxcosx+acos^2x
=1/2SIN2X+a(1+cos2x)/2
=1/2SIN2X+a/2 cos2x+a/2
=√(1/4+a²/4)sin(2x+m)+a/2
由 f(x)=√(1/4+a²/4)+a/2=1+(根号3)/2
得：a=√3
∴f(x)=sin(2x+π/3)+√3/2
∴ T=π
(2)由2kπ+π/2≤2x+π/3≤2kπ+3π/2,k∈Z
得：kπ+π/12≤ x≤kπ+7π/12,k∈Z
∴f(x）单调递减区间为【kπ+π/12,kπ+7π/12】,k∈Z
（3）由2x+π/3=kπ,k∈Z得：x=kπ/2-π/6,k∈Z
∴对称中心(kπ/2-π/6,√3/2)k∈Z
2x+π/3=kπ+π/2,k∈Z 得：x=kπ/2+π/12,k∈Z
∴对称轴方程 x=kπ/2+π/12,k∈Z