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 6x sin 2x

Video transcript

Hello. Today we're going to be simplifying the given product by using the sum to product identity. So what we are given is sine of 128 alpha multiplied by sine of 74 alpha. We can utilize the sign, the sign sum to product identity to simplify the given product and the sum to product identity. For sign states that if we have a product of sign of a multiplied by sine of B, we can rewrite the product as one half multiplied by the quantity cosine of A minus B minus cosine of A plus B. Here, we're going to allow our A value to equal to 128 alpha. And we're going to allow B to equal to 74 alpha. If we utilize the identity and the given A and B values, we can rewrite our original product as one half multiplied by the quantity cosine of 128 alpha minus 74 alpha minus cosine of 128 alpha plus 74 alpha. Now, what we wanna do is we want to simplify the angles of cosine 128 alpha minus 74 alpha will give us the value of 54 alpha and alpha plus 74 alpha will give us the value of 202 alpha. So we can further simplify the quantity as one half multiplied by the quantity cosine of 54 alpha minus cosine of 202 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 a. 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.