2sin(x+π／3)+2a－1＝0在〔0,π〕上有2个不等实数根,求a取值范围

2sin(x+π/3)+2a-1=0,得sin(x+π/3)=1/2-a 在[0,π]上,当0≤x≤π/6时,sin(x+π/3)单调递增 在[0,π]上,当π/6≤x≤π时,sin(x+π/3)单调递减 则在[0,π]上,sin(x+π/3)有最大值sin(π/6+π/3)=1、最小值sin(π+π/3)=-√3/2 即-√3/2≤sin(x+π/3)≤1 即-√3/2≤1/2-a≤1 得a的取值范围[-1/2,(1+√3)/2]huosin(x+π／3)=1/2-a π／3