(1)
f(x)＝(1+cos2x)/2+(1/2)sin2x
＝(√2/2)sin(2x+π/4)+1/2.
∴sin(2x+π/4)＝1时,
y|min＝(1+√2)/2.
(2)
f(A/2+π/8)＝1,
∴(√2/2)sin[2(A/2+π/8)+π/8]+1/2＝1
→sin(A+3π/8)＝√2/2
→A+3π/8＝3π/4
→A＝3π/8.
∴三角形面积S＝(1/2)·3·3·sin(3π/8)