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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
a better way
Page 1 | Page 2 | Page 3 | Proof(s)

Example 4--Page 3

Still, using our compare strategy, we know 6_4302.gif (1590 bytes)6_4303.gif (1880 bytes) should equal to 6_4304.gif (1631 bytes). You can tell that this is not abusive. What is the difference? The operations are different. There are 4 terms in the parenthesis, we should combine them. How could we do that? By combining -1 and 6_4305.gif (1378 bytes) we get cos_4tht.gif (1198 bytes), which is a like term with another cos_4tht.gif (1198 bytes). You might see that cos_4tht.gif (1198 bytes)6_4306.gif (1626 bytes), which is one of the Double Angle formulas.

6_4307.gif (8986 bytes)

Again, use our compare strategy, 6_4308.gif (1671 bytes) should equal to 6_4309.gif (1623 bytes). It’s just the Sum to Product formula.

The identity has been proven.

6_4310.gif (4048 bytes)

The main idea in proving this problem is to compare both sides often so we will know what's the next step. Always try to get closer to what we want. Once you find out what you need, use formulas to get it. It sounds easy, but try to think about it and make sure you understand what we mean. And think how you can reach your target.


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Copyright 1998 LWR, ThinkQuest team 17119. All rights reserved.