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先看一个例题: 例1 证明tg3°tg17°tg23°tg37°tg43°××tg57°tg63°tg77°tg83° tg27°初看起来等式左边很有规律:3°、17°、23°、27°…,然而一旦动手做,你便会觉得这些数字与“27”很难联系,因而难以凑效,有兴趣的读者不妨先试一试。有一个三角等式却对证明这道题大有用处。这个等式就是:tg3a=tgatg(π/3-a)tg(π/3+a)关于这个等式的证明很简单,只须两边分别展开比较即得。下面应用它来证明上例:
First look at an example: Example 1 prove that tg3 ° tg17 ° tg23 ° tg37 ° tg43 ° x tg57 ° tg63 ° tg77 ° tg83 ° tg27 ° at first glance left equation is very regular: 3 °, 17 °, 23 °, 27 °... However, once you do it, you will find it difficult to connect these numbers with the “27” and it is difficult to work. Interested readers may wish to try it first. There is a triangle equation that is of great use to prove this problem. The equation is: tg3a=tgatg(π/3-a)tg(π/3+a) The proof of this equation is very simple. It only needs to be compared on both sides. Use it below to prove the example: