tan2θ-tanθ和tanθ哪个大同上

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tan2θ-tanθ和tanθ哪个大同上tan2θ-tanθ和tanθ哪个大同上tan2θ-tanθ和tanθ哪个大同上解tan2θ-tanθ-tanθ=tan2θ-2tanθ=2tanθ/(1-ta

tan2θ-tanθ和tanθ哪个大同上
tan2θ-tanθ和tanθ哪个大
同上

tan2θ-tanθ和tanθ哪个大同上
解tan2θ-tanθ-tanθ
=tan2θ-2tanθ
=2tanθ/(1-tan^2θ)-2tanθ
=2tanθ[1/(1-tan^2θ)-1]
=2tanθ[(1-(1-tan^2θ))/(1-tan^2θ)]
=2tanθ[tan^2θ/(1-tan^2θ)]
=2tan^3θ/(1-tan^2θ)
知tanθ>1时,2tan^3θ/(1-tan^2θ)<0,即tan2θ-tanθ<tanθ,
当0<tanθ<1时,2tan^3θ/(1-tan^2θ)>0,即tan2θ-tanθ>tanθ
当-1<tanθ<0时,2tan^3θ/(1-tan^2θ)<0,即tan2θ-tanθ<tanθ
当tanθ<-1时,2tan^3θ/(1-tan^2θ)>0,即tan2θ-tanθ>tanθ