Answer:
(1+cos(theta))/(1-sin^2(theta))=sec(theta)+tan^2(theta)+1
(1+cos(theta))/cos^2(theta)=sec(theta)+sec^2(theta)-1+1
(1-cos(theta))/cos^2(theta)=1/cos(theta)+1/cos^2(theta)
1-cos(theta)=cos(theta)+1
2cos(theta)=0
cos(theta)=0
theta=pi/2 and 3pi/2
I don't fully understand your question but it's quite easy to solve. As shown above, option (2) is good and you can factor the RHS but I would find it rather trivial when you can multiply both sides by cos^2(theta) just as easily. I hope this helps you.
