Introduction
   Essence
   Memorizing
   Understanding
   Summarizing
   Examples

Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
General ideas

   Exercises
   Final thoughts

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?