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
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![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](/uploads/image/z/7448265-9-5.jpg?t=%E8%AF%81%E6%98%8E%2Ctanatan2a%2Ftan2a-tana%3Dsin2a%3D2%7Bsina%2Fcosa%7D%2Fcos%5E2a%2Fcos%5E2%2Bsin%5E2%2Fcos%5E2%E5%88%86%E5%AD%90%E5%88%86%E6%AF%8D%E5%90%8C%E6%97%B6%E6%88%90cos%5E2%3D+%5B2tan%CE%B1%C2%B7%28cos%CE%B1%29%5E2%5D%2F%5B%28cos%CE%B1%29%5E2+%2B+%28sin%CE%B1%29%5E2%5D%3D+%282sin%CE%B1cos%CE%B1%29%2F1%3D+sin2%CE%B1)
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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
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
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
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.
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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
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