Worksheets evolve. At least, I think they ought to: every tool that is used to assist learning can be refined, clarified, formatted better, made more interesting, extended and just generally improved. That's certainly been the case with my worksheet on trigonometric expansions. It started life when I first saw a very elegant geometric proof for the tan(a+b) identity (which is equal to (tana + tanb)/(1  tanatanb), if you're curious). When I was in year 11, I learnt this identity by rote, not thinking that there would be any value in understanding where it originated from. (In fact, at that stage, I didn't even realise that I possessed the necessary knowledge or conceptual framework to derive this result at all. I now know that it's well within the reach of a Year 10 trigonometry standard.) So to see it gracefully demonstrated in very simple terms was an eyeopener for me. (It may be strange for you to know that, despite going to James Ruse and even studying a full maths degree at university, I only really started learning maths when I began to teach it. There's a real lesson in there for all people who really want to learn what they are studying. I think there's a stronger causal relationship between teaching and learning than studying and learning!) I immediately set out to convert what I'd seen into a handout that students could go through. And so the worksheet was born  and here are the stages it went through in its development:

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