Question

sinα+cosα=(1-根号下3)/2，α∈0,π，求tanα

如题……要过程 ① ②式联解，得sinα=1/2, cosα=-√3/2 这是怎么算出来的？？？我咋就算不出来这两个数呢……搞出来个根号里面还有根号……算不出数啊……

Answer 1

tan2θ=2根号2，0<2θ<2π
0<2θ<π/2或π<2θ<3π/2sinθ
2sin^2θ/2-1/√2cos(π/4-θ）=sinθ-(1-2sin^2θ/2)
1-1/2cosπ/4cos(π/4-θ)=sinθ-cosθ
1-1/(cos(π/2-θ)
cosθ)=sinθ-cosθ
1-1/(sinθ
cosθ)=(sin^2θ-cos^2θ-1)/(sinθ
cosθ)
1=(-cos2θ-1)/(sinθ
cosθ)
1cos2θ=1/3或-1/3
sin2θ=2根号2/3或-2根号2/3cosθ=根号6/3或-根号6/3，sinθ=根号3/3原式=（-1/3-1）/（根号3/3
根号6/3）=-4/（根号3
根号6）=-4（根号6-根号3）/3或=（1/3-1）/（根号3/3-根号6/3）=-2/（根号3-根号6）=2（根号6
根号3）/3