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### [Index]

Introduction
Essence
Memorizing
 How to memorize Basic Formulas Sum and Difference Formulas Double & Triple Angle Formulas Half Angle Formulas Product to Sum Formulas Sum to Product Formulas All Formulas
Understanding
 Page 1 Page 2 Page 3 Page 4 Page 5
Summarizing
 Page 1 Page 2
Examples
 Examples Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 7 Example 8 General ideas
Exercises
Final thoughts
Page 1 | Page 2 | Proof(s)

### Example 2

The difference of angles is sharp. The right side has no , so first we want to cancel in left side.

If you read our Memorizing the formulas section, this problem should not be a hard one for you because we included three Triple Angle formulas there. Two of these we will use here. Namely, and .

We see we can factor from , and from . Thus we can simplify and . By using the Triple Angle formulas we get:

Being very straight forward, we want to factor out and , at the top of the two fractions respectively, and cancel it with the bottom.

Then combine the like terms, we have

We know can help us to cancel , so we factor out -4, we get,

The identity has been proven.

It's not hard right? Without knowing our idea you can do it too, but can you give another proof?