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1. IntroductionFirst, as hosts, we welcome you to Trigonometric IdentitiesA Clever Way to Prove. If you are reading this, we believe that you are interested in mathematics, or that you want to improve your mathematics problem solving skill.Well, mathematics is interesting and very powerful. A lot of people have lost their confidence while studying it, however. Is math hard? Maybe, it depends on how you look at it, and how you learn it. 1 + 1 = 2? That's right. Is it easy? Yes. When you look at the problem, at the same time, you know the answer. Let's try 3 + 5 + 7 = 15. Yes, it takes you a couple of more seconds to think about it, but finally you know the answer. What we are trying to say is that when we know the most basic things, or ideas, even though a problem is more complicated, we still have good chances to solve it. Equality proving is one of the most basic problems in mathematics. If we know how the equality works, then we will know how to evaluate, solve equations and so on. Trigonometry has a lot of different kinds of formulas. Some of them are really complex. This makes trigonometric problems a great example to discuss. As students, we have heard our friends and other students talking about math: "I can not do it." "I do not know how to do it." or "It's too hard." without even looking at and thinking about the problems. People are really scared by mathematics. In general, the structures of a trigonometry book are definitions, formulas, and examples. Most are examples about how to apply formulas directly to some problems and are only for those particular formulas. This arrangement has some defects. For example, we can always see some students who don't know how to start to prove an identity without any hint even if they know every trigonometric formula. Here at LWR, we try to complete all trigonometry books. We are not giving you a bunch of questions. Instead, we give you some general ideas to prove an identity, and by that way we can improve your mathematics problem solving skills. We try to help you make a big improvement in a short period of time. We believe our ideas are the best, and we need you to prove that we are the best. Before we begin, you must ask yourself: "Do I really want to improve my problem solving skills?" If the answer is yes, then you are ready to go. ThinkQuest team 17119, LWR 

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