I was working on a differential equations homework problem and it took me a few tries to remember how to simplify a trig expression. So, I thought I’d put the results here to remind myself and others about trigexpand().
The second order linear equation is
Now I asked my students to use the identities
to write the equation equivalently as
Finally, I wanted to use Maxima to show these two expressions are equivalent. I reflexively used trigsimp() on the difference between the two expression (the name says it all, am I right?) but the result was complicated in a way that I couldn’t recover…certainly not zero as I hoped. A few minutes of thought and I remembered trigexpand() which, followed by a call to trigsimp(), gives the proof: