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Express the given sum or difference as a product of sines andlor cosines sin 7x - sinxsin 7x - sinx = (Simplify your answer: )Enter your answer in the answer box:...

Question

Express the given sum or difference as a product of sines andlor cosines sin 7x - sinxsin 7x - sinx = (Simplify your answer: )Enter your answer in the answer box:

Express the given sum or difference as a product of sines andlor cosines sin 7x - sinx sin 7x - sinx = (Simplify your answer: ) Enter your answer in the answer box:



Answers

Rewrite the sum or difference as a product. $$\sin (3 x)+\sin (7 x)$$

We need to convert the difference that is. Sign seven X minus Signed three x into a product formula. Now we know that sign A minus sign B is equal toe, so sign a minus bi divided by two multiplied with course off a plus B divided by two. So using this formula will get equal to you'll sign. Seven X minus three Excavated by two multiplied with course off seven X plus three x Divided by two which will become equal toe to sign for extirpated by two. Multiplied with course off an X divided by two, which will be equal to two. Signed two x multiplied with because five x.

We have from 44. Love 44 23 in this military right? The same as a product. So the question is saying three X. Place Sign seven X. This is like sign you plus sign D. Which is equal to to sign hopelessly by two. Cause human is the way to where this is you. This is v. Two saying you bless we buy two. And of course Human is the right to of course you minus V. Right to So to sign 10 x by two cause -4 X x two. This is fine. This is true. So this is to sign five X. Cause -2X. It will simply because two weeks. So they should be the answer. Thank you.

So for this question, were given co signed seven X Plus Co. Sign Negative seven X Um, and we're asked to wreck. This is a product. So before we begin, I think it's important to note that co sign is that even function. So you know that CO sign X is equal to co sign negative X. This is just a proper name. Even functions would change that. We can rewrite this as co sign of seven x plus coastline seven x and, uh, combine these two. Then we get to co sign seven X and we're done.

Okay, so we want to rewrite the falling A product. So let's use our some to product for me long for sign one's son. So we get to co sign of, um however inside that's two x plus seven X over two. And then we also have coast on of two X minus seven X over two. Okay, so let's simplify that. So we get two plus seven. That's nine X over two, and then we have co sign of negative five X over two. So don't hear that or recall here. That co sign is and even function. So we have. If we have co sign of negative X, that's equal to CO side of X. Okay, so we can rewrite that as to co sign of nine x over two and then co sign of five x over two


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