工作之余,将部分题目改编整合,使之与2005有机结合.下给几例,供同学们练习.1.设f(sinx)=sin2005x.求证:f(cosx)=cos2005x.2.数列{an}满足下列条件:a1=2;当n为奇数时,an+1=an+2;当n为偶数时,an+1=2an.求a2005.3.证明log20052004·log20052006<1.4.已知x+(1/(x-1))=3.求的值.下面给出以上各题的简解,供参考. In the spare time, we will reorganize and integrate some of the topics and integrate them with 2005. Give a few examples for the students to practice. 1. Set f(sinx)=sin2005x. Prove: f(cosx)=cos2005x.2. An} satisfies the following conditions: a1=2; when n is odd, an+1=an+2; when n is even, an+1=2an. find a2005.3. Proof log20052004·log20052006<1.4. Known x+(1/(x-1))=3. The value obtained. The following gives a brief explanation of the above questions for reference.