(tanαtan2α)/(tan2α-tanα)化简急
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/08/08 05:27:50
(tanαtan2α)/(tan2α-tanα)化简急
![(tanαtan2α)/(tan2α-tanα)化简急](/uploads/image/z/19996703-71-3.jpg?t=%28tan%CE%B1tan2%CE%B1%29%2F%28tan2%CE%B1-tan%CE%B1%29%E5%8C%96%E7%AE%80%E6%80%A5)
因tanα=tan(2α-α)=(tan2α-tanα)/(1+tan2αtanα)
故(tanαtan2α)/(tan2α-tanα)=(tanαtan2α)/[(1+tan2αtanα)*tanα]=tan2α/(1+tan2αtanα)
=sin2αcosα/(cos2αcosα+sin2αsinα)=sin2αcosα/cosα=sin2α
故(tanαtan2α)/(tan2α-tanα)=(tanαtan2α)/[(1+tan2αtanα)*tanα]=tan2α/(1+tan2αtanα)
=sin2αcosα/(cos2αcosα+sin2αsinα)=sin2αcosα/cosα=sin2α
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