（1）
cos²x=1/2(1+cos2x),
sinxcosx=1/2sin2x
∴f(x)=1/4(1+cos2x)+√3/4sin2x+1
=1/4cos2x+√3/4sin2x+5/4
=1/2(√3/2sin2x+1/2cos2x)+5/4
=1/2sin(2x+π/6)+5/4
f(x)的最小正周期T=2π/2=π
(2)
∵x∈[π/12,π/4]
∴2x∈[π/6,π/2]
∴2x+π/6∈[π/3,2π/3]
∴当2x+π/6=π/2,即x=π/6时,
sin(2x+π/6)=1,f(x)max=7/4
当2x+π/6=π/3,或2x+π/6=2π/3时,
,即x=π/12或x=π/4时,
sin(2x+π/6)=√3/2,f(x)min=(√3+5)/4
（3）
f(A)=1/2sin(2A+π/6)+5/4=3/2
sin(2A+π/6)=1/2
∵0