text: I remember having trouble with these types of problems too.  There's so many trig identities to choose from, it's hard to know sometimes what to use!\n\nSince there's no trig identity (that I know of) for secx + tanx, I think I'd multiply my fraction by (secx-tanx) / (secx-tanx) to see if I can get rid of the denominator.  (A trick that sometimes works when you have a-b in the denominator is to multiply top and bottom by a+b so that you get a²-b² in the denominator.):\n\n1 / (secx + tanx) = \n\n(secx - tanx) / (secx + tanx)(secx - tanx) =\n\n(secx - tanx) / (sec²x - tan²x)\n\nNow I would use the trig identity tan²x + 1 = sec²2 (because notice this can be rewritten as 1 = sec²x - tan²x).  So ....\n\n(secx - tanx) / (sec²x - tan²x) = \n\n(secx - tanx) / 1 =\n\nsecx - tanx\n\nHope that helped!\n\n~ ♥ ~