(1) f（x）=sin²ωx+√3sinωsin（ωx+π/2）
=1/2-1/2cos2wx+√3/2sin2wx
=1/2+sin(2wx-π/6)
π=2π/2w
解之：w=1
所以：f(x)=1/2+sin(2x-π/6)
(2) f(x)+f(x+2)=2sin(π/4x+π/4)+2sin(π/4x+π/2+π/4)
=2sin(π/4x+π/4)+2cos(π/4x+π/4)
=2√2cos(π/4x)
所以：f(x)+f(x+2)最大值在x=-2/3时取得；其值为-√6/3
f(x)+f(x+2)最小值在x=-6是取得；其值为-2√2.