若|x|≤π/4,求函数y=2sin|x+π/3|-2sinx的最值
问题描述：
若|x|≤π/4,求函数y=2sin|x+π/3|-2sinx的最值
答
|x|≤π/4-π/4≤x≤π/4∴x+π/3>0∴y=2sin|x+π/3|-2sinx=2sin(x+π/3)-2sinx=2(sinx*1/2+cosx*√3/2)-2sinx=sinx+√3cosx-2sinx=√3cosx-sinx=2(cosx*√3/2-sinx*1/2)=2cos(x+π/6)-π/4≤x≤π/4∴-π/12≤x+π/...