In Exercises 45–46, express each sum or difference as a product. ...

Question

In Exercises 45–46, express each sum or difference as a product. If possible, find this product's exact value.sin 2x - sin 4x

Accepted Answer

Hello, everyone. We are asked to use a sum to product formula to rate the following expression as a product. The sign of 36 X minus the sign of X. We are given four answer choices. First recall the sum to product formulas. So we know we have a formula that is the sign of alpha minus. The sign of beta will equal two multiplied by the sign of alpha minus beta divided by two multiplied by the cosine of alpha plus beta divided by two. So how does this apply? In this example? We're gonna say that alpha is 36 X and beta is 38 X. So when we are thinking of the sign of X minus the sign of 38 X, we can use our identity and say it's two multiplied by the sign of alpha. So 36 X minus beta which is X divided by two and then multiplied by the cosine of alpha. So 36 X plus beta which is 38 X divided by two. I'm going to simplify, simplify my fractions. So two multiplied by the sign of 36 X minus 38 X is negative two X divided by two. And then the cosine of 36 X plus 38 X would be 74 X divided by two. And we can simplify those fractions a little further. So we have two multiplied by the sign of negative X cosine of 37 X. And I'm gonna factor the negative out from in front of the X and bring it in front of the two. So we are left with negative two sine X cosine 37 X. And I'm gonna just make sure I group my XS and my numbers together and I am left with negative two multiplied by the sign of X multiplied by the cosine of 37 X which is answer choice C have a nice day.

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In Exercises 45–46, express each sum or difference as a product. If possible, find this product's exact value.sin 2x - sin 4x

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