(sinα +cosα)²=sin²α+cos²α+2sinα *cosα=1+2sinα *cosα=(1-√3)²/4=1-(√3)/2sinα *cosα=-(√3)/4sinα[(1-√3)/2-sinα]=-(√3)/4sin²α-(1/2-√3/2)sinα-√3/4=0(sinα+√3/2)(sinα-1/2)=0sinα=1/2或sinα=-√3/2(不在0<α<π上,舍去)cosα=-√3/2tan=-√3/3