化简(1-√3tanθ)sec(θ+π/3)cosθ=?
问题描述：
化简(1-√3tanθ)sec(θ+π/3)cosθ=?
答
sec(θ+π/3)=1/cos(θ+π/3)=1/(cosθcosπ/3-sinθsinπ/3)=1/(cpsθ/2-√3sinθ/2)
=2/(cosθ-√3sinθ)
sec(θ+π/3)cosθ=2cosθ/(cosθ-√3sinθ)=2/(1-√3tanθ)
(1-√3tanθ)sec(θ+π/3)cosθ=(1-√3tanθ)2/(1-√3tanθ)=2
答
(1-√3tanθ)sec(θ+π/3)cosθ
=2*(1/2*cosθ-√3/2sinθ)/cosθ/cos(θ+π/3)*cosθ
=2(cos(π/3)cosθ-sin(π/3)sinθ)/cos(θ+π/3)
=2cos(θ+π/3)/cos(θ+π/3)
=2