Now we could recall that cot(x) = 1/tan(x)
therefore, cot(arctan(x)) = 1/[tan(arctan(x))] = 1/x ........since the tan undoes the arctan
but here is a general method of how to approach these problems when they don't work out so nicely.
We wish to find
but the tangent ratio is given by the ratio of the side opposite the angle to the side adjacent to the angle, thus we can construct the triangle you see below. We draw the angle theta and fill in the opposite and adjacent side accordingly. We can find the hypotenuse using Pythagoras' theorem, but that was not needed here.
Now you try the others