Question

已知sinθ,cosθ是方程x2-(√(3)-1)+m两根求1)m的值 2)[sinθ/(1-cotθ)]+[cosθ/

Answer 1

1.根据韦达定理：sinθ+cosθ=√3 - 1 , sinθcosθ=m

∵sin²θ+cos²θ=1

∴sin²θ+cos²θ=(sinθ+cosθ)² - 2sinθcosθ=(√3 - 1)² - 2m =4 - 2√3 - 2m=1

m=(3/2) - √3

2.[sinθ/(1-cotθ)]+[cosθ/(1-tanθ)]={sinθ/[1-(cosθ/sinθ)]} + {cosθ/[1-(sinθ/cosθ)]}

={sinθ/[(sinθ/sinθ)-(cosθ/sinθ)]} + {cosθ/[(cosθ/cosθ)-(sinθ/cosθ)]}

=[sin²θ/(sinθ-cosθ)] + [cos²θ/(cosθ-sinθ)]

=[sin²θ/(sinθ-cosθ)] - [cos²θ/(sinθ-cosθ)]

=(sin²θ-cos²θ)/(sinθ-cosθ)

=sinθ+cosθ

=√3 - 1