问题标题：
已知函数f(x)=2sin平方(派/6x)+sin((派/3x+派/6)-1,求f(x)值域
问题描述：
已知函数f(x)=2sin平方(派/6x)+sin((派/3x+派/6)-1,求f(x)值域
陈飞回答：
f(x)=2sin2(π/6x)+sin(π/3x+π/6)-1
=sin(π/3x+π/6)-[1-2sin2(π/6x)]
=sin(π/3x+π/6)-cos(π/3x)
=sin(π/3x)*cosπ/6+cos(π/3x)sinπ/6-cos(π/3x)
=sin(π/3x)*√3/2+1/2cos(π/3x)-cos(π/3x)
=sin(π/3x)*√3/2-1/2cos(π/3x)
=sin(π/3x-π/6)
-1≤sin(π/3x-π/6)≤1
f(x)值域为:[-1,1]
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