证明,tanatan2a/tan2a-tana=sin2a

题目

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

答案

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]}= ...