已知函数f(x)=sin(wx+π/6)+sin(wx-6/π)-2cos^2(wx/2) 求值域 若函数图像与直线Y=

f(x)
=sin(wx+π/6)+sin(wx-6/π)-2cos^2(wx/2)
=sin(wx)* √3/2+cow(wx)*1/2+sin(wx)*√3/2-cos(wx)*1/2-(cos(wx)+1)
=sin(wx)*√3-cos(wx)-1
=2*sin(wx-π/6)-1
所以
-3≤f(x)≤1
f(x)=-1时,sin(wx-π/6)=0,x=(n+1/6)π/w
间距π/2,所以w=2
所以f(x)=2sin(2x-π/6)-1
单调递增区间为：2nπ-1/2π ≤ 2x-π/6 ≤ 2nπ+1/2π
所以 nπ-1/6π ≤ x ≤ nπ+1/3π

f(x)=2sinwx cosπ/6-1-coswx
=2(sinwx cosπ/6- coswx sinπ/6)-1
=2sin(wx-π/6)-1
f max=1,f min=-3
值域[-3,1]
f(x)=2sin(2x-π/6)-1
kπ+π/2=2x-π/6
2x= kπ+2π/3
对称轴方程x= kπ/2+π/3，k∈Z