2x²-(√3+1)x+m=0的两根分别为sinθ - 知识问答

2x²-(√3+1)x+m=0的两根分别为sinθ,cosθ 求(sinθtanθ)/(tanθ-1)+cosθ/(1-

1个回答

由韦达定理知sinθ+cosθ=（√3+1）/2,
所以(sinθtanθ)/(tanθ-1)+cosθ/(1-tanθ)
=sin²θ/(sinθ-cosθ)-cos²θ/(sinθ-cosθ)
=(sin²θ-cos²θ)/(sinθ-cosθ)
=sinθ+cosθ
=（√3+1）/2

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