Be sure that you've familiarized yourself with the second set of ...

Question

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value.

cos 4x + cos 2x

Accepted Answer

Hello, everyone. We are asked to rate the given trigonometric sum as a product. We are given cosine of 10 X plus the cosine of six X. There are four answer choices. First recall that the cosine of A plus, the cosine of B would equal two multiplied by the cosine of A plus B divided by two multiplied by the cosine of A minus B divided by two. In our example, A is 10 X B is six X. So we are gonna plug 10 X and six X in for A and B. So we get two multiplied by the cosine of 10 X plus six X divided by two multiplied by the cosine of 10 X minus six X divided by two. I'm going to combine my like terms in my numerators. So I have two multiplied by the cosine of X divided by two multiplied by the cosine of four X divided by two and I can reduce those fractions. So I will and I'll have two multiplied by the cosine of eight X multiplied by the cosine of two X. This appears to be everything that I can simplify. So this is our product two multiplied by the cosine of eight X multiplied by the cosine of two X which is answer choice D have a nice day.

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Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. cos 4x + cos 2x