题干

给出如下四个命题

①对于任意的实数α和β,等式cos(α+β)=cosαcosβ﹣sinαsinβ恒成立;
②存在实数α,β,使等式cos(α+β)=cosαcosβ+sinαsinβ能成立;
③公式tan(α+β)= tantantantan
α
+
β
1
−
α
⋅
β
成立的条件是α≠kπ+
π
2
(k∈Z)且β≠kπ+
π
2
(k∈Z);
④不存在无穷多个α和β,使sin(α﹣β)=sinαcosβ﹣cosαsinβ;
其中假命题是(   )

A:①②

B:②③

C:③④

D:②③④

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答案(点此获取答案解析)

C

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    Being a sports reporter for more than a decade, I see “Olympic” as a1word to me. I found the word is also a(an)2for everyone to shine. This feeling3me when I was holding the Olympic torch for the4time on Monday in Seoul, the capital city of South Korea.

    I felt such a great5to be invited by the International Olympic Committee to be a torchbearer for the 2018 Pyeongchang Winter Games 6Chinese sports reporters. Ten years ago, I was invited by IOC to be a7for the 2008 Beijing Summer Games. I have now carried the torch in two different countries. I have 8how the Olympic flame 9everybody around it.

    When I arrived at the 10point for the torchbearers, all the staff and even passers-by cheered because they knew I would be joining the11. I could feel their heartfelt12 toward the Olympics. When a group of torchbearers left to join in the relay, all the people13 shouting “Fighting!” While I14my turn, many people came to take photos with me and the torch. In 101 days, the route15nine provinces and eight major cities across the country. With less than a month to go before the Games1 opening ceremonies in Pyeongchang, Seoul had been16 into an Olympic city as well.

    “Let everyone shine' is not just a slogan for the torch relay but 17the fact that ordinary people from every walk of life—students, bakers, teachers, farmer —are18.The Olympic spirit is a lot more than the19 of 'swifter, higher, and stronger.' 'Olympic, has the magic to bring everyone together to20their dreams.