Cases inside table

Question

So, I want to display cases inside a table. This is my Latex document, as minimized as I could to reproduce the problem. Apparently, it says:

(./redundant.aux)
! Missing $ inserted.
<inserted text> 
                $
l.12 \begin{cases}

I don't get it. The cases environment works totally fine outside tables. What's wrong with my Latex code and how do I fix it?

\documentclass[11pt, fullpage, lefteqn]{article} 
\usepackage{amsmath}

\begin{document}
\begin{table}[h!]
\centering
\begin{tabular}{|c|c|}
 \hline
  $a^2 - x^2$
            & 
\[
\begin{cases}
a \sin x \\ a \cos x
\end{cases}
\] & \\
\end{tabular}
\end{table}
\end{document}

Edit: when I try to change the cs to ps, I get

! Missing number, treated as zero.
<to be read again> 
                   |
l.9   $
       a^2 - x^2$

Answer 1

Vertical display material like \[ needs to be in a par (vertical) mode column such as p or m

\documentclass[11pt, 
%fullpage, % article does not have fullpage or lefteqnoptions
%lefteqn
leqno
]{article} 
\usepackage{amsmath}
\usepackage{array}% for m

\begin{document}
\begin{table}[htp] % [h!]
\centering
\begin{tabular}{|c|m{5cm}|}
 \hline
  $a^2 - x^2$
            & 
\[
\begin{cases}
a \sin x \\ a \cos x
\end{cases}
\] \\
\hline
\end{tabular}
\end{table}
\end{document}