(tan(x)+sec(x)-1)/(tan(x)-sec(x)+1)

Question

to prove:

(tan(x)+sec(x)-1)/(tan(x)-sec(x)+1)=sec(x)+tan(x)

Answer 1

cross multiply, let t=tanx, s= secx

t^2 -st +st +t + s - s^2= t+s-1

or

t^2-s^2 + t + s = t+s -1

t^2 - s^2 = -1

t+s -1 = t+ s -1