Two of these identities turn a product into a sum and two turn a sum into a product. They come straight out of adding and subtracting the sum and difference formulas.
The identity gives sin of the sum plus sin of the difference.
The sum is 8x and the difference is minus 2x.
Sine of minus 2x is minus sin 2x.
The answer is sin8x−sin2x.
Where students go wrong
Dropping the sign on the difference. Sine of a negative angle is negative, so sin(A − B) with B larger than A flips: cosine would not, and mixing the two rules up is the usual slip.
Also called sum to product, product to sum formulas or trig identities.
What you can put on this worksheet
Product to sum
2sin4xcos5x→ sin9x−sinx
Sum to product
sin8x+sin6x→ 2sin7xcosx
Questions about these worksheets
Yes. Every product to sum identities sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the product to sum identities questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 2: product to sum and sum to product. Tick as many as you want and set how many of each, or let it spread them evenly.
Dropping the sign on the difference. Sine of a negative angle is negative, so sin(A − B) with B larger than A flips: cosine would not, and mixing the two rules up is the usual slip.