作业帮证明,tanatan2a/tan2a-tana=sin2a
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/05/01 12:14:41
证明,tanatan2a/tan2a-tana=sin2a
=2{sina/cosa}/cos^2a/cos^2+sin^2/cos^2
分子分母同时成cos^2
= [2tanα·(cosα)^2]/[(cosα)^2 + (sinα)^2]
= (2sinαcosα)/1
= sin2α
=2{sina/cosa}/cos^2a/cos^2+sin^2/cos^2
分子分母同时成cos^2
= [2tanα·(cosα)^2]/[(cosα)^2 + (sinα)^2]
= (2sinαcosα)/1
= sin2α
分子 = tanα·tan2α = tanα·2tanα/[1 - (tanα)^2] ,分母 = tan2α - tanα = 2tanα/[1 - (tanα)^2] - tanα ,分子分母同时乘以 [1 - (tanα)^2] ,
原式 = tanα·2tanα/{2tanα - tanα·[1 - (tanα)^2]}
= 2(tanα)^2/[tanα + (tanα)^3]
= 2tanα/[1 + (tanα)^2]
= [2tanα·(cosα)^2]/[(cosα)^2 + (sinα)^2]
= (2sinαcosα)/1
= sin2α
证毕.
原式 = tanα·2tanα/{2tanα - tanα·[1 - (tanα)^2]}
= 2(tanα)^2/[tanα + (tanα)^3]
= 2tanα/[1 + (tanα)^2]
= [2tanα·(cosα)^2]/[(cosα)^2 + (sinα)^2]
= (2sinαcosα)/1
= sin2α
证毕.
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