1+cos2θ+2sin²θ=1+cos2θ+1-(1-2sin²θ)=2+cos2θ-cos2θ=2
(1-cos2θ)/(1+cos2θ)=(1-(1-2sin²θ))/(1+(2cos²θ-1))=2sin²θ/(2cos²θ)=tan²θ