LaTeX/Beamer, column environment. Horizontal alignment of overlays - latex

Question

I am trying to prepare a presentation using beamer. I want to have two columns that walkthrough some algebraic manipulations. On the left an explanation of the steps taken, on the right the results.
\documentclass{beamer}
\begin{document}
\begin{frame}[t]
Not in a column
\begin{columns}[t]
\begin{column}{0.5\textwidth}
\only<2->{Some text}
\only<3->{
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
}
\end{column}
\begin{column}{0.5\textwidth}
\only<2->
{
\begin{equation}
E = mc^2
\end{equation}
}
\only<3->
{
\begin{equation}
F = ma
\end{equation}
}
\end{column}
\end{columns}
\end{frame}
\end{document}
And here's some LaTeX which does that (with junk words and equations). When this is compiled the text and maths are not aligned with each other. I wouldn't really expect them to be either as LaTeX will position the text in each column individually, not caring about the other frames.
Does anyone have any ideas on how to achieve the result I am after. I'm not committed to the columns at all, but I am committed to the equation numbers.

Answer 1

The preferred way to get aligned equations with numbering is amsmath package's align environment. See its documentation for help with that. It's quite simple, something like:
\begin{align}
f(x) & = \cos^2 x \\
g(x) & = \sin^2 x
\end{align}
There are a lot of variations trying to cover most conceivable equation alignment needs (again, check out the documentation).
As for your two-column proof format, I'm not as sure about the best way. A quick and dirty way would be to add it as a second column within the environment, something like:
\begin{align}
f(x) & = \cos^2 x & \text{this is the first function} \\
g(x) & = \sin^2 x & \text{this is the second function}
\end{align}
but this is no good for multi-line explanation, and puts the numbering to the right of the text. I'll try and think of a way (one that doesn't involve a lot of custom-defined environments, since surely someone's done this before).
Edit: As a starting point, this [sort of] works:
You can't do any alignment within the align environment (the & confuses things), and there are some vertical alignment issues - the align environment pads itself above and below, and the text in the right-hand cell. Maybe it's heading in a good direction, though!
\begin{tabular}{p{3 in}|l}
\begin{align} f(x) = \sin^2 x \end{align} &
this is the first equation \\
\begin{align} g(x) = \cos^2 x \end{align} &
this is the second equation
\end{tabular}

Answer 2

Usually you'd use amsmath's align or align* environment, but unfortunately it doesn't play nicely with beamer (for fundamental reasons that nobody wants to fix).
The Beamer user guide has a section on this at page 106 that does exactly what you've done. Apparently there's a workaround described in that document too.