若tan(π/4-θ)=3,则(cos2θ)/(1+sin2θ)等于?

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若tan(π/4-θ)=3,则(cos2θ)/(1+sin2θ)等于?若tan(π/4-θ)=3,则(cos2θ)/(1+sin2θ)等于?若tan(π/4-θ)=3,则(cos2θ)/(1+sin2

若tan(π/4-θ)=3,则(cos2θ)/(1+sin2θ)等于?
若tan(π/4-θ)=3,则(cos2θ)/(1+sin2θ)等于?

若tan(π/4-θ)=3,则(cos2θ)/(1+sin2θ)等于?
tan(π/4 - θ) = 3
[tan(π/4) - tanθ]/ [1 + tan(π/4) tanθ] = 3
(1- tanθ) / (1 + tanθ) = 3
tanθ = -1/2
cos2θ/(1 + sin2θ)
= [(1 - tan²θ)/(1 + tan²θ)] / [1 + 2tanθ/(1 + tan²θ)]
= (1 - tan²θ) / (1 + tan²θ + 2tanθ)
= 3