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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
Page 1
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Page 3
Page 4
Page 5
Page 1
Page 2
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
General ideas
Final thoughts

4. Understanding the formulas--Page 4

Using the Sum and Difference formulas, we can easily get the Derived formulas.

4_402.gif (2321 bytes), if k is an odd integer,

4_403.gif (2193 bytes), if k is an even integer.

Here T can be any trigonometric functions, and co-T is the co-function of function T. For example, sine and cosine are co-functions of each other, similarly tangent and cotangent, secant and cosecant respectively.

For example

4_404.gif (5398 bytes)

and so on, all of such formulas can proved by the Sum and Difference formulas:

4_405.gif (3525 bytes),

since     4_406.gif (1917 bytes).

4_407.gif (3389 bytes)

since     4_408.gif (1795 bytes), and so on.  In the same way we can prove all of them.


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