How to memorize the sum-to-product and product-to-sum formulae more easily ??

I know how to deduce the formula but when i try to memorize it, its so hard. Always sin, cos, a+b, a-b, i always get confused. Is there any way to memorize more efficiently??

for the sin(A±B) and cos(a±B)

for the Sine is goes sinAcosB ± cosAsinB
and for Cosine is goes cosAcosB ... sinAsinB

for the Sine, the signs stay the same,
that is, sin(A+B) = sinAcosB + cosAsinB and
sin(A-B) = sinAcosB - cosAsinB

In the cosine formula, the signs are opposite, that is
cos(A+B) = cosAcosB - sinAsinB and
cos(A-B) = cosAcosB + sinAsinB

Write them down a few times, keep the order A,B always in that order, and also say them out-loud
Sine ... sincos cossin
cosine .... coscos sinsin

for sines, signs stay the same,
for cosine, signs switch

well, i think u have mistaken my question.

what i meant is i cant memorize the sum-to-product formula and product to sum formula, which are
Review
Product to Sum Formulas

1. sin x cos y = (1/2) [ sin(x + y) + sin(x - y) ]

2. cos x sin y = (1/2) [ sin(x + y) - sin(x - y) ]

3. cos x cos y = (1/2) [ cos(x + y) + cos(x - y) ]

4. sin x sin y = (1/2) [ cos(x - y) - cos(x + y) ]

Sum to Product Formulas

1. sin x + sin y = 2*sin[ (x + y) / 2 ]*cos[ (x - y) / 2 ]

2. sin x - sin y = 2*cos[ (x + y) / 2 ]*sin[ (x - y) / 2 ]

3. cos x + cos y = 2*cos[ (x + y) / 2 ]*cos[ (x - y) / 2 ]

4. cos x - cos y = 2*sin[ (x + y) / 2 ]*sin[ (x - y) / 2 ]

1. sin x + sin y = 2*sin[ (x + y) / 2 ]*cos[ (x - y) / 2 ]

2. sin x - sin y = 2*cos[ (x + y) / 2 ]*sin[ (x - y) / 2 ]

3. cos x + cos y = 2*cos[ (x + y) / 2 ]*cos[ (x - y) / 2 ]

4. cos x - cos y = 2*sin[ (x + y) / 2 ]*sin[ (x - y) / 2 ]

Sorry for bothering you again :)

I am usually pretty old-fashioned in my mathematical outlook, but in this case for these 12 formulas, I would not expect my students to memorize these rather low-priority formulas.

Geesh, I even had to look some of these up myself.

I am curious what level of math you are studying and at what college.

i am in my grade 11 and study in asia

Memorizing formulas can be challenging, but there are a few strategies you can use to make it easier. Here are some tips to help you memorize the sum-to-product and product-to-sum formulas more efficiently:

1. Understand the derivation: Before attempting to memorize the formulas, it's essential to fully understand how they are derived. By understanding the logic and reasoning behind them, you'll have a stronger foundation to build upon.

2. Break it down: Instead of trying to memorize the entire formula all at once, break it down into smaller parts. Focus on understanding the individual components, such as the functions (sin, cos) and the arithmetic operations (addition, subtraction, multiplication).

3. Visualize: Create visual representations of the formulas. Draw diagrams or flowcharts that illustrate how each part of the formula relates to one another. Visual aids can help reinforce your understanding and make the information easier to remember.

4. Mnemonics: Associate the formulas with memorable phrases or acronyms. Create a mnemonic device that summarizes the key components of the formula. For example, for the sum-to-product formula sin(a) + sin(b) = 2sin((a+b)/2)cos((a-b)/2), you could use the mnemonic "Triple S, Double C" to represent "2sin((a+b)/2)cos((a-b)/2)."

5. Practice with examples: Apply the formulas to actual examples or problem-solving exercises. By using the formulas in practice, you reinforce your understanding and help commit them to memory. Additionally, working through examples can help you identify patterns or common calculations that aid in memorization.

6. Repetition and review: Regularly review the formulas to reinforce your memory. Set aside dedicated study sessions where you focus solely on practicing and reciting the formulas. Repetition is key to solidifying your memorization.

7. Utilize flashcards or mnemonic devices: Transform the formulas into flashcards or mnemonic devices. Write one side with the formula and the other side with the mnemonic or reminder for each component. Regularly review these flashcards to strengthen your memory.

8. Create connections: Find connections between the formulas and other concepts or formulas you are already comfortable with. By creating associations between different mathematical ideas, you can leverage your existing knowledge to aid in the memorization process.

Remember, it's natural for memorization to take time and practice. Be patient with yourself, and don't get discouraged if it doesn't happen instantly. With consistent effort and using these strategies, you can improve your ability to memorize and recall the sum-to-product and product-to-sum formulas more efficiently.