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   Introduction Introduction
   What's the essence? Essence
   Memorizing Memorizing
   Understanding Understanding
   Summarizing Summarizing
   Examples Examples

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

   Exercises Exercises
   Final thoughts Final thoughts
Page 1 | Page 2 | Proof(s)

Example 6

6_6101.gif (6744 bytes)

Actually this is a kind of conditional identity, because it has the actual angles. If the angles change, this identity may not be true. In some identities, it doesn't matter what are the angles. You should know that none of the angles in this problem are special angles. They are not like pi_o_2.gif (955 bytes), pi_o_3.gif (945 bytes), pi_o_4.gif (950 bytes), and pi_o_6.gif (943 bytes), so we can't convert their functions to special numbers. If there are conditions for a given identity, we will need to use them when we prove the identity, or it's none sense to have conditions. We will use the conditions--the angles pi_o_7.gif (938 bytes), 2pi_o_7.gif (1024 bytes), etc, to prove this identity.

After comparing the two sides we see that the big difference is the difference of operations. To reduce it, we will combine the terms on the left.

6_6102.gif (5061 bytes)

By comparing what we get with the right side, we believe that 6_6103.gif (3965 bytes)6_6104.gif (1236 bytes), because we already get 6_6105.gif (1570 bytes). If we can prove that, then the problem is solved. So we separate the left to two factors.

6_6106.gif (5744 bytes)


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