Given events $E_1,E_2,E_3,...,E_n$ and $A$, I know that $\displaystyle P(E_k|A)=\frac{P(E_k∩A)}{P(A)}$. However sometimes the Bayes' theorem is used instead: $\displaystyle P(E_k|A)=\frac{P(A|E_k)P(E_k)}{\sum_{i=1}^{n} P(A|E_i)P(E_i)}$.
When I get a problem, how can I recognize which one to use?
As per my understanding both are equivalent and one has to check that the information given in the question is used in which equation and use that equation accordingly.
My teacher was telling that the first equation is used when we are given one event in addition to $A$ and the second equation is used when we are given more than one event in addition to $A$ but I cannot understand why. I think that both the equations can be used for any number of events in addition to $A$.
I am confused. Please help.
As stated in a comment by user247327, your chosen method depends on what is given to you in the question. If you are already given $P(A)$, then you can use the first form. However, often you aren't given this, but instead you're given $P(A|E_k)$ and $P(E_k)$. Then you have to use the second form, where you are essentially using this information to work out $P(A)$ anyway.
I.e, they are both saying the same thing - it is true that $$P(A)=\sum_k P(A|E_k)P(E_k)$$ where $E_k$ are a disjoint collection of events whose union is the entire sample space $\Omega$ (this condition is always satisfied by the events they give in those kinds of problems).