(1-cot^2theta)/(1+cot^2theta)+2cos^2theta1−cot2θ1+cot2θ+2cos2θ
= (1-cos^2theta/sin^2theta)/(1+cos^2theta/sin^2theta)+2cos^2theta1−cos2θsin2θ1+cos2θsin2θ+2cos2θ
= ((sin^2theta-cos^2theta)/sin^2theta)/((sin^2theta+cos^2theta)/sin^2theta)+2cos^2thetasin2θ−cos2θsin2θsin2θ+cos2θsin2θ+2cos2θ
= ((sin^2theta-cos^2theta)/sin^2theta)xx(sin^2theta/(sin^2theta+cos^2theta))+2cos^2theta(sin2θ−cos2θsin2θ)×(sin2θsin2θ+cos2θ)+2cos2θ
= (sin^2theta-cos^2theta)/cancel(sin^2theta)xxcancel(sin^2theta)/1+2cos^2theta
= sin^2theta-cos^2theta+2cos^2theta
= sin^2theta+cos^2theta=1