已知函数f(x)=2sinwx*coswx+2根号3cos^2wx-根号3(其中w>0),直线x=x1,x=x2是y=f

1)
(f(x)=2sinwx*coswx+2根号3cos^2wx-根号3
=sin2wx+√3(1+cos2wx)-√3
= sin2wx+√3cos2wx
=2(1/2*sn2wx+√3/2*cos2wx)
=2sin(2wx+π/3)
∵直线x=x1,x=x2时对称轴
|x1-x2|的最小值为π/2.
∴T/2=π/2,T=π
由2π/(2w)=π ∴w=1
(2)
f(a)=2/3
∴2sin(2a+π/3)=2/3
∴sin(2a+π/3)=1/3
sin(5π/6-4a)=sin(-4a+π/2+π/3)=cos(π/3-4a)
=cos[π-(2π/3+4a)]=-cos(4a+2π/3)
=2sin²(2a+π/3)-1=2*1/9-1=-7/9