arctan(x) is the inverse function of tan(x), and it means that, if y=arctan(x), then y is a number such that tan(y)=x.
In general, f is the inverse function of g if f(g(x))=g(f(x))=x.
On the other hand, cot(x) simply is 1/tan(x), so it's simply the inverse number of tan(x).
So, you have that, as a function, arctan(x) is the inverse of tan(x), which means that composing the two functions results in the identity function. In formulas,
artan(tan(x))=tan(arctan(x)=x.
Instead, as a number (i.e. you must fix x), cot(x) is the inverse of tan(x), which means that multiplying the two numbers gives one as a result:
tan(x)cot(x)=1 for every x.
