Suppose that I have equation:

$$\tan(a) = \dfrac{b-c}{bc + 1},\;\text{ where }\,a, b, c\, \text{ are variables.}$$

How can I show that, as $a \to \pi/2, \; bc+1\to 0\;$ mathematically, not intuitively.

I know how to calculate limit, as variable $(X,Y)$ approaches to $(X\_0,Y\_0)$, but not the other way. 

How can I find point where $(X,Y)$ approaches, when the limit is given, mathematically rather than intuitively?