f(x)=cos(2x-π/3)+sin(x-π/4)sin(x+π/4)
= cos(2x-π/3)-sin(π/4-x)sin(x+π/4)
= cos(2x-π/3)-cos(x+π/4)sin(x+π/4)
=(1/2)cos2x+(√3/2)sin2x-(1/2)sin(2x+π/2)
=(1/2)cos2x+(√3/2)sin2x-(1/2)cos2x
= (√3/2)sin2x,
∴最小正周期T=π,
令2x=kπ+π/2,k∈Z,
得x=kπ/2+π/4,k∈Z,
∴图象的对称轴方程为x=kπ/2+π/4,k∈Z,
当x∈[-π/12,π/2]时,2x∈[-π/6,π],sin2x∈[-1/2,1],
∴值域为[-(√3/4),√3/2].