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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 3

In order to understand formulas very well, we should also know the relationships between some formulas. For example, we get the Sum and Difference formulas from the definitions of trigonometric functions. From Sum formulas, let = = , then we get the Double-Angle formulas. From Double-Angle formulas of cosine:

we get Half-Angle formulas:

In fact the relationship of and is double angle relationship. Sometimes, the following formulas:

are very useful. Also we know:

by adding these two formulas, we can get:

 (1)

Let , . If we add them together, we have , . From (1), we have: .

 (2)

After substituting x and y by and respectively in (2), we have the Sum to Product formula:

From (1) divide by 2 on both sides, we have the Product-to-Sum formula: