(1)
sin(wx+π/6)=sinwxcosπ/6+coswxsinπ/6
sin(wx-π/6)=sinwxcosπ/6-coswxsinπ/6
f(x)=sin(wx+π/6)+sin(wx-π/6)-2cos²wx/2
f(x)=sinwx-2cos²wx/2
f(x)=√3sinwx-coswx-1
f(x)=2[(√3/2)sinwx-(1/2)coswx]-1
f(x)=2(sinwxcosπ/6-sinπ/6coswx)-1
f(x)=2sin(wx- π/6)-1
1≥f(x)≥-3
x屬于（a,a+π）的圖像與直線y=-1有且僅有一個(gè)交點(diǎn)
可得f(x)的周期為2π,所以w=1
（2）
f(x)=2sin(x- π/6)-1
因?yàn)閟inx的單調(diào)增區(qū)間是
2kπ-π/2≤x≤2kπ+π/2
不等式各邊同時(shí)減π/6
2kπ-π/2-π/6≤x-π/6≤2kπ+π/2-π/6
2kπ-2π/3≤x-π/6≤2kπ+π/3
所以f(x)=2sin(x- π/6)-1的單調(diào)增區(qū)間是[2kπ-2π/3,2kπ+π/3]