问题 解答题
已知sin22α+sin 2αcos α-cos 2α=1,α∈(0,
π
2
),求sin α、tan α的值.
答案

由sin22α+sin2αcosα-cos2α=1,得

4sin2αcos2α+2sinαcos2α-2cos2α=0

2cos2α(2sin2α+sinα-1)=0

2cos2α(2sinα-1)(sinα+1)=0.

因为α∈(0,

π
2
),所以sinα+1≠0,且cosα≠0,

所以2sinα-1=0,即sinα=

1
2

所以α=

π
6
,即tanα=
3
3

填空题
材料分析题

李明是某校九年级学生。暑假的一天,他和叔叔家上小学的弟弟李浩做完作业到大街上玩。在村委会大院中,他看到墙上的选民榜中有爸爸妈妈和爷爷奶奶等人的名字。在公告栏中,他看到自己的叔叔还是乡人大代表的候选人。这时,弟弟李浩缠着他问:“上面怎么没有咱俩的名字呢?” 回到家,爷爷告诉李明他要在选举日那天慎重地投出自己的一票。可是奶奶却说:“都这么大年纪了,管他谁当选呢,用不着操那份闲心。”

(1)假如你是李明,你该怎样给李浩作出解释呢?

                                                                                                                                                             

                                                                                                                                                             

                                                                                                                                                            

(2)假如你是李明,你可以用哪些知识来劝说奶奶?

                                                                                                                                                            

                                                                                                                                                             

                                                                                                                                                             

(3)假如李明的叔叔被选为乡人大代表,你觉得李明可以向叔叔说些什么?