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

Question

Be sure that you've familiarized yourself with the first set of formulas presented in this section by working C1–C4 in the Concept and Vocabulary Check. In Exercises 1–8, use the appropriate formula to express each product as a sum or difference.

sin x cos 2x

Accepted Answer

Hello, everyone. We are asked to convert the given trigonometric expression into an equivalent expression using a product to some identity. We are given the sign of 35 X multiplied by the cosine of 38 X. We have four answer choices. First, I recall that we have an identity about when we have the sign of one angle multiplied by the cosine of another. So the sign of A multiplied by the cosine of B and the identity states that, that equals one half multiplied by square bracket. Sign of A plus B closed parentheses plus the sign of A minus B closed parentheses, closed square bracket. So in this example, A is gonna be 35 X and B is 38 X. So let's plug that in and we have one half multiplied by the square bracket inside. We have the sign of A plus B. So A plus B so 35 X plus X closed parentheses plus the sign of A minus B. So 35 X minus 38 X closed parentheses, close square bracket. I'm gonna combine my like terms within the parentheses. So I have one half multiplied by the square bracket sign of, let's see, this is 73 X plus the sign of negative three X closed parentheses, closed square bracket. I don't want the negative within my parentheses. So I'm gonna factor that out in front of my second sign. So we will have one half multiplied by the square bracket sign of 73 X closed parentheses. And now we're gonna do minus the sign of three X closed parentheses, closed square bracket. And this should give us our answer. There is nothing else we can simplify. So one half multiplied by the square bracket, sign of 73 X minus the sign of three X is our answer. And that is answer choice. A have a nice day.

Be sure that you've familiarized yourself with the first set of formulas presented in this section by working C1–C4 in the Concept and Vocabulary Check. In Exercises 1–8, use the appropriate formula to express each product as a sum or difference. sin x cos 2x

Key Concepts

Product-to-Sum Formulas

Trigonometric Identities

Angle Addition and Subtraction

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