How does one determine: $$\cos^2(\arctan(x))?$$
I know what it is equal to, since its in the tables. But without working with many trigonometric identities, its not clear how to find such things.
How would you see this with the minimal number of trig identities?
The one identity I used here, I didn't know. It seems in similar situations, on an exam, I would have massive trouble without these identities. Can all of these sorts of things be solved by knowing something about Eulers identity and such?