论文部分内容阅读
1987年全国成人高校统一招生数学(文史类)试题的第六题是:证明sin~22x++2cos~2xcos2x=2cos~2x,标准答案为: 左端=(2sinxcosx)~2+2cos~2x(cos~2x--sin~2x)=4sin~2x cos~2x+2cos~4x-2sin~2xcos~2x=2cos~2x(sin~2x+cos~2x)=2cos~2x=右端。 (证法一) 该题证法很多,只要掌握sin2x=2sinxcosx,cos2x=cos~2x-sin~2x=2cos~2x-1=1-2sin~2x及sin~2x+cos~2x=1,则可以从不同角度入手证出,试举几种如下: 证法二
In 1987, the sixth question of the mathematics (arts and history) examination questions for the national adult colleges and universities was: proof sin~22x++2cos~2xcos2x=2cos~2x, the standard answer is: left end=(2sinxcosx)~2+2cos~2x(cos ~2x--sin~2x)=4sin~2x cos~2x+2cos~4x-2sin~2xcos~2x=2cos~2x(sin~2x+cos~2x)=2cos~2x=right. (Certificate A) This is a lot of questions, as long as you master sin2x=2sinxcosx, cos2x=cos~2x-sin~2x=2cos~2x-1=1-2sin~2x and sin~2x+cos~2x=1, You can start from different angles to prove that you can try several of the following: