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### [Index]

Introduction
Essence
Memorizing

Basic Formulas
Sum and Difference Formulas
Double & Triple Angle Formulas
Half Angle Formulas
Product to Sum Formulas
Sum to Product Formulas
All Formulas

Understanding
Summarizing
Examples
Exercises
Final thoughts

## Double-Angle Formulas:

In Sum and Difference formulas, if and are the same angle, which we let them equal to , then you get these Double Angle formulas. Also, a 2 always appears in the formulas, as a coefficient 2 or as a square. The term is a term that shows up a lot (3 times). Being strong in these formulas will make solving identities a lot easier. The term is also common in real problems.

Formula 1, the product of mixed functions sine and cosine, just don't forget the coefficient 2.

Formula 2, remember that on the right side cosine and sine are all squared and it is the square of cosine minus the square of sine. Be aware of the order of the subtraction. Try to compare with .

Formulas 3 and 4 come from formula 2 by using . Notice the order of the terms: equals to but not ; but not . Later, in Understanding the Formulas we will talk more about this.

Formula 5, from the Sum formulas of tangent we can easily get this one when angle = = .

There is also one more thing we want to mention, which is the Triple Angle formulas. They are not in most books, but we want to let you know them, because sometime you will need them to prove identities.