This trig problem kept me up too late last night

My daughter is taking a precalc summer school course. Last night she was doing her homework, which was about verifying trigonometric identities. Out of the 25 homework problems, there was one that she got stuck on. I decided to give it a try and spent two hours on it without solving it.

Here it is. Verify the identity:

(sec x - tan x)² = (1 - sin x )/(1 + sin x )

You don't need to know anything about trigonometry to solve this. All you need to know are the fundamental trigonometric identities, which are:

My daughter is in class now and she texted me the answer. There's not too many steps involved. Let's see how fast you can solve it.