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.

sin 7x ﹣ sin 3x

Accepted Answer

Hello, everyone. We are asked to rate the given trigonometric difference as a product. We are given the sign of nine X minus the sign of five X. There are four answer choices. First recall the formula for the difference of signs. So we have the sign of A minus, the sign of B equals two multiplied by the sign of A minus B divided by two multiplied by the cosine of A plus B divided by two. In our example, A will be nine X and B will be five X. So we are gonna plug this into the formula. So we have two multiplied by the sign of nine X minus five X divided by two multiplied by the cosine of nine X plus five X divided by two. I'm going to combine my like terms in the numerators and we will have sign, oh, I'm sorry, two multiplied by the sign of four X divided by two multiplied by the cosine of 14 X divided by two. And when I simplify my fractions, I will have two multiplied by the sign of two X cosine of seven X. And that looks like as far as we can simplify this. So our product is two multiplied by the sign of two X multiplied by the cosine of seven X and that matches 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. sin 7x ﹣ sin 3x