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. cos 7x cos 3x

Video transcript

Hello. Today we're gonna be rewriting the given expression by using an identity. So what we are given is cosine of alpha multiplied by cosine of 29 alpha. Now, we can rewrite this expression by using the sum to product property of cosine the sum to product property of cosine states that if we have the form of cosine of a multiplied by cosine of B, this product can be rewritten as one half multiplied by the quantity of cosine A minus B plus cosine of A plus B. If we want to utilize this, this identity, we're going to allow A to equal to 71 alpha and we're going to allow B to equal to 29 alpha. And if we utilize the identity and the A and B values, we can rewrite the given product as one half multiplied by the quantity cosine of A which is 71 alpha minus B, which is 29 alpha plus cosine of A which is 71 alpha plus B which is alpha. Now, what we wanna do is we want to simplify the given angles. So 71 alpha minus 29 alpha will give us the value of 42 alpha and alpha plus 29 alpha will give us the value of alpha. That means we can rewrite the expression as one half multiplied by the quantity cosine of 42 alpha plus cosine of 100 alpha. And this is going to be the simplified form of the given product. And with that being said, the answer to this problem is going to be B so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.