Prove that Tan theta + Sec theta – 1 / Tan theta – Sec theta + 1 = 1+Sin theta / Cos theta @EAG

Prove that Tan theta + Sec theta – 1 / Tan theta – Sec theta + 1 = 1+Sin theta / Cos theta @EAG

Solution: T + S - 1 / T - S + 1
= T + S - 1 / T - S + (Sec² - Tan²)
= T + S - 1 / (S - T)(– 1 + S + T)
= 1 / S – T
Now rationalize the Dr. with S + T
Then it become as below
= S + T / (S + T)(S – T)
= S + T / 1 (Since (S+T)(S-T) = 1)
= S + T
= 1 / Cos + Sin / Cos
= 1 + Sin / Cos
Thank you student

[Ruthvik]

Sir why denominator should write as it is pls Sir I can't understand.