Chapter 23
Ten Not-So-Basic Identities
IN THIS CHAPTER
Using products to find sums
Going vice versa: Finding products from sums
Reducing from two functions to one
Equating parts of triangles to trig functions
In Chapters 10 and 11, I cover the most frequently used identities at great length. Here are ten identities that don’t appear in those chapters, because you won’t use them all that often. A few are rather obscure. These identities don’t lend themselves to memorization very well — you’ll be better off just looking them up if you need them.
Product-to-Sum Identities
The product-to-sum identities look very much alike. You have to pay close attention to the subtle differences so that you can apply them correctly. Even though the product looks nice and compact, it’s not always as easy to deal with in calculus computations — the sum or difference of two different angles is preferred.
The first identity has two angles, A and B. When you multiply the sine of one angle times the cosine of the other angle, you end up with one-half the sum of a sum identity and a difference identity. ...
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