三角函数题一道,急一道中档题.已知▲ABC中,角A、B、C所对的边分别为a、b、c,若A、B、C成等差数列,b=1,记角

B=180°/3=60°
A+C=120°
正弦定理:
sinx/a=sin(2π/3-x)/c=sin60°/1=√3/2
a+c=(2√3/3 ){sinx+sin(2π/3-x)}=cosx+√3sinx=2sin(x+π/6)
f(x)=2sin(x+π/6)
【1】当x∈[(π/6),(π/3)],
f(x)的取值范围[2sin(π/3),2sin(π/2)]即[√3,2 ]
【2】若f(x-π/6)=6/5,求sin2x的值
f(x-π/6)=2sin(x)=5/6
sinx=5/12
cosx=√(1-25/144)=√119/12
sin2x=2sinxcosx=2*(5/12)*(√119/12)=5√119/72
)