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### [Index]

Introduction
Essence
Memorizing
Understanding

Page 2
Page 3
Page 4
Page 5

Summarizing
Examples
Exercises
Final thoughts

### 4. Understanding the formulas--Page 2

We know the Double-Angle formula of cosine:

which show us the relationship between angles and . These three presentations are not different essentially. Using the formula , we can get one form from other two forms. Now from the idea of transforming the three differences, we understand how to use these three formulas. If we want to transform to and cosine to sine, we use the second form. If we want to change to and keep the function cosine, we use the third form, if we want to change to and cosine to cosine and sine we use the first form.

The Sum to Product formulas are as following:

In section 3, we told you how to memorize these four formulas. Of course, the first role of these formulas is changing sum to product from the left to the right. Now we need to know what kinds of functions can transform to the others, and as well as the angles. From the formulas we see, sine plus or minus sine changes to sine times cosine; cosine plus cosine to cosine times cosine; cosine minus cosine to sine times sine; and , to and .

We can not explain every formula for you. We believe that you can analyze every formula like we did. After you read our eliciting explanation above, please complete the analysis of all formulas, which is important for you to solve problems.