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Fill in the blank to complete the trigonometric formula.
$ \cos u - \cos v $ = ________
$-2 \sin \frac{u+v}{2} \sin \frac{u-v}{2}$
00:24
Amy J.
Precalculus
Algebra
Chapter 5
Analytic Trigonometry
Section 5
Multiple-Angle and Product-to-Sum Formulas
Trigonometry
Introduction to Trigonometry
McMaster University
Harvey Mudd College
Idaho State University
Lectures
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Fill in the blank to …
So we want to look at what is the identity that takes co sign of you minus cosine of the And this is although it's a difference. It's listed as one of the some to product forms, and so if we think of it that way, we can see it's, ah, some or plus negative. It's a difference. You know, you're right down forms that this will equal negative two times the sign, interestingly enough, and it's a product. They're gonna be a product of two functions. Both will be sign, and we take u plus V over to so basically finding the average of the angles times the sign of U minus to be over to. And not that this question asked this. But remember that if you have this being a plus, it's not as simple as just saying, Oh, just change this to a plus. It becomes a totally different formula, but it's still going to be a product of two functions, but that becomes the product of the cosine of the same angle you plus B over to times the cosine of U minus v over to. So this is the one that with the question is asking about. So we're going from a difference to a product
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