I need to prove that: $1+\tan x \tan 2x = \sec 2x.$
I started this by making sec 1/cos and using the double angle identity for that and it didn't work at all in any way ever. Not sure why I can't do that, but something was wrong.
Anyways I looked at the solutions manual and they magic out $1 + \tan x \tan 2x = 1+\tan x\left(\frac{2 \tan x}{1-\tan ^2x}\right) $ which I recognize as the double angle forumla sort of, I just don't understand why I can use that and how they magiced it into this. It is just too difficult to think of an equation in an equation in an equation. I tried working with this and got nowhere near the right answer.