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 6x sin 4x

Accepted Answer

Hello, everyone. We are gonna 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 22 X multiplied by the sign of 18 X. We are given four answer choices. First, recall our product to some formulas. If we have the sign of one angle measure, calling it alpha multiplied by the sign of another angle measure, we'll call it beta. The formula that, that equals is one half multiplied by in parentheses or in this case, square brackets, the cosine of alpha minus beta minus the cosine of alpha plus beta close brackets. So in our example, we again have the sign of 22 X multiplied by the sign of 18 X. So for our example, alpha will be 22 X and beta will be 18 X. So plugging this into the formula we are given. So we have one half multiplied by a square bracket and then the cosine of open parentheses alpha. So 22 X minus beta, 18 X closed parentheses minus the cosine of open parentheses alpha which is X plus beta, which is 18 X closed parentheses, close square brackets to simplify this a little bit more. I'm gonna do the sums and differences of the alpha and beta values. So we will have one half and it will be multiplied by. And I'm gonna use parentheses now and then cosign of 22 X minus 18 X is four X minus the cosine of 22 X plus X which is 40 X closed parentheses. So this is our expression one half multiplied by the parentheses cosine of four X minus the cosine of 40 X. And this matches answer choice C have a nice day.

In Exercises 43–44, express each product as a sum or difference. sin 6x sin 4x

Key Concepts

Product-to-Sum Formulas

Sine Function Properties

Angle Addition and Subtraction Identities

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