Prove that 1+tan(Theta)/1-tan(Theta) = sec^2(Theta)+2tan(Theta)/1-tan^2(Theta)

Question

If you explain, that would be great (:

Answer 1

(1+tan)/(1-tan)

multiply top and bottom by 1+tan

(1+tan)^2 / (1-tan)(1+tan)

(1 + 2tan + tan^2)/(1-tan^2)

now, since sec^2 = 1+tan^2,

(sec^2 + 2tan)/(1-tan^2)