已知sinα+cosα=（1-√3）/2α∈（0,π）.求tanα的值

Question

已知sinα+cosα=（1-√3）/2 α∈（0,π）.求tanα的值

Answer 1

sinα+cosα=(1-√3)/2<0,且α∈(0,π),则α∈(3π/4,π),2α∈(3π/2,2π),
(sinα+cosα)^2=1-(√3)/2
2sinαcosα=-(√3)/2
sin2α=-(√3)/2
2α=(5π)/3
α=(5π)/6
tanα=-(√3)/3