(1)、f(x)=2cos²x-（sinx-cosx）²
=2cos²x-(1-sin2x)
=cos2x+sin2x
运用一下化一公式得f(x)=√2sin(2x+π/4),T(min)=2π/2=π
(2)、将x=a/2带入f(x)=√2sin(2x+π/4)中得f(a/2)=√2sin(a+π/4)=√2
则有 sin(a+π/4)=1
∵a∈[0.π/2],∴(a+π/4)∈[π/4,3π/4],可推出(a+π/4)=π/2,即a=π/4
则tan(a+π/3)=tan(π/4+π/3)=[tan(π/4）+tan（π/3)]/[1-tan(π/4)tan(π/3)]=-2-√3