Thank you, it's been a very long couple of weeks >.<

the secant thing, I just made a careless error on, upon review, I see your answer is correct.

And good eye on pulling out the t in the denominator, that's definitely why my answer was so far off from theirs. You'd think I'd remember to check such things :/

The negative on the derivative of csc(a) came because I don't have that function's integral memorized, so I just went to look it up by typing it into the calculator. It told me:

out of annoyance with myself for not just figuring it out, I went to figure it out just now... and I'm having a tough time of it, can you show me how to it?