In Exercises 43–44, express each product as a sum or difference.
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Question

In Exercises 43–44, express each product as a sum or difference.

sin 7x cos 3x

Accepted Answer

Hello, everyone. We are going to use a product to sum formula to write the following expression as a sum or a difference. The expression we are given is the sign of 15 X multiplied by the cosine of nine X. We are given four answer choices. First recall your product to some formula when we have a sign multiplied by a cosine. It is that the sign of alpha multiplied by the cosine of beta equals one half multiplied by the sign of alpha plus beta plus the sign of alpha minus beta. So in our example, we are again given the sign of 15 X multiplied by the cosine of nine X. So this means alpha for this example would be X and beta is nine X. So now that I know this, I'm gonna plug it into this formula. So I have one half, it's gonna be multiplied by the sign of alpha plus beta. So 15 X plus nine X closed parentheses. And then I'm adding the sign of alpha again, 15 X minus beta. So nine X close parentheses and I'm gonna close my square bracket. I wanna see if I can simplify what is in the parentheses next to the sign function. So I have one half and I'm opening a square bracket. And in that I will have the sign of 15 X plus nine X. So 24 X plus the sign of 15 X minus nine X. So that would be six X and I closed my square bracket. I can replace my square brackets with parentheses because I no longer have multiple sets of grouping symbols. And when I do, I get one half multiplied by the parentheses. Sine of 24 X plus sine of six X closed parentheses. This is our sum that will use the product to some formula and it matches answer choice a have a nice day.

In Exercises 43–44, express each product as a sum or difference. sin 7x cos 3x

Key Concepts

Product-to-Sum Formulas

Sine and Cosine Functions

Angle Addition and Subtraction

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