作业帮设集合A={x|x≠kπ,且x≠kπ+π/2,k∈z}已知a=[2cos(α+β)/2,sin(α－β)/2],b=[cos(α+β)/2,3sin(α－β)/2]其中α,β∈A（1）若α+β=2π/3且a=2b,求α,β的值（2）若a?b=5/2,求tanαtanβ的值还有能不能写的明白点、有些
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![设集合A={x|x≠kπ,且x≠kπ+π/2,k∈z}已知a=[2cos(α+β)/2,sin(α－β)/2],b=[cos(α+β)/2,3sin(α－β)/2]其中α,β∈A（1）若α+β=2π/3且a=2b,求α,β的值（2）若a?b=5/2,求tanαtanβ的值还有能不能写的明白点、有些](/uploads/image/z/8957179-19-9.jpg?t=%E8%AE%BE%E9%9B%86%E5%90%88A%3D%7Bx%7Cx%E2%89%A0k%CF%80%2C%E4%B8%94x%E2%89%A0k%CF%80%2B%CF%80%2F2%2Ck%E2%88%88z%7D%E5%B7%B2%E7%9F%A5a%3D%5B2cos%28%CE%B1%2B%CE%B2%29%2F2%2Csin%28%CE%B1%EF%BC%8D%CE%B2%29%2F2%5D%2Cb%3D%5Bcos%28%CE%B1%2B%CE%B2%29%2F2%2C3sin%28%CE%B1%EF%BC%8D%CE%B2%29%2F2%5D%E5%85%B6%E4%B8%AD%CE%B1%2C%CE%B2%E2%88%88A%EF%BC%881%EF%BC%89%E8%8B%A5%CE%B1%2B%CE%B2%3D2%CF%80%2F3%E4%B8%94a%3D2b%2C%E6%B1%82%CE%B1%2C%CE%B2%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E8%8B%A5a%3Fb%3D5%2F2%2C%E6%B1%82tan%CE%B1tan%CE%B2%E7%9A%84%E5%80%BC%E8%BF%98%E6%9C%89%E8%83%BD%E4%B8%8D%E8%83%BD%E5%86%99%E7%9A%84%E6%98%8E%E7%99%BD%E7%82%B9%E3%80%81%E6%9C%89%E4%BA%9B)
设集合A={x|x≠kπ,且x≠kπ+π/2,k∈z}已知a=[2cos(α+β)/2,sin(α－β)/2],b=[cos(α+β)/2,3sin(α－β)/2]其中α,β∈A（1）若α+β=2π/3且a=2b,求α,β的值（2）若a?b=5/2,求tanαtanβ的值还有能不能写的明白点、有些
设集合A={x|x≠kπ,且x≠kπ+π/2,k∈z}已知a=[2cos(α+β)/2,sin(α－β)/2],b=[cos(α+β)/2,3sin(α－β)/2]其中α,β∈A
（1）若α+β=2π/3且a=2b,求α,β的值
（2）若a?b=5/2,求tanαtanβ的值
还有能不能写的明白点、有些回答说实话看不懂= =
（2）里面那个问号打错了 是乘号
设集合A={x|x≠kπ,且x≠kπ+π/2,k∈z}已知a=[2cos(α+β)/2,sin(α－β)/2],b=[cos(α+β)/2,3sin(α－β)/2]其中α,β∈A（1）若α+β=2π/3且a=2b,求α,β的值（2）若a?b=5/2,求tanαtanβ的值还有能不能写的明白点、有些
（1）因为a=2b
则2cos(α+β)/2=2cos(α+β)/2
sin(α－β)/2=2*3sin(α－β)/2=6sin(α－β)/2
即5sin(α－β)/2=0
sin(α－β)/2=0
所以(α－β)/2=kπ k∈z α－β=2kπ k∈z ①
根据题意 α+β=2π/3 ②
由①②可求得：α=kπ +π/3 k∈z
β=π/3-kπ k∈z
（2）a*b=5/2
则2cos(α+β)/2*cos(α+β)/2+sin(α－β)/2*3sin(α－β)/2=2cos(α+β)/2^2+3sin(α－β)/2^2=1+cos(α+β)+3/2*(1-cos(α-β))=1+cosacosb-sinasinb+3/2-3/2*(cosacosb+sinasinb)=5/2-1/2*cosacosb-5/2*sinasinb=5/2
cosacosb=-5sinasinb
tanαtanβ=(sinasinb)/(cosacosb)=-1/5