Verify:

Question

Tan u + sec u-1 / tan u - sec u+1 = tan u + sec u

Answer 1

You have

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

multiply top and bottom by tan+sec-1 and you have

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

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

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

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

tan+sec

Answer 2

Two steps after multiplying the top and bottom, why does tan become 2tan on top

Answer 3

tan does not become 2tan

expand (a+b-1)^2 and you will see the 2's, just as

(a+b)^2 = a^2 + 2ab + b^2