Any trick to remember the Product-to-sum and sum-to-product identities?

Maybe look up how people in memory competitions memorize things. I think memory skills are one of the most misunderstood things. There's a tendency to try to reduce a memory task to as few "bits" of information as possible. This is actually effective, but it's not always possible and it's only half of the story. What you want to do is create stories, meanings, associations, and so on with what you're trying to memorize. I've memorized many trigonometric identities and derivatives around the narrative that cosine is a self-centered jerk. I also learned how to derive the formulas, because that's actually mathematically important. In high school I told a friend an inappropriate sentence that made it clear what the gas laws were for Boyle's, Charle's, and Gay-Lussac's, and in a way that you knew which was which (because that was the point). Neither of us have studied chemistry in college or since but we have never forgotten these formula-name associations. It's basically impossible to forget at this point. Sometimes I tutored chemistry so when I did that I knew them without needing to think of the sentence, but after I would stop tutoring chemistry for a long stretch that same sentence would still be there and immediately yield the proper associations.

So memorize more, not less. Reducing the core or seed of what needs to be known to involve as little information as possible makes sense, but beyond that memorize more. Make up stories. Anything emotionally evocative or meaningful is even better, regardless of whether it's positive or negative (so long as it doesn't harm you of course).

/r/learnmath Thread