若tanα=3,tanβ=4/3,则tan﹙α-β﹚等于__?

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若tanα=3,tanβ=4/3,则tan﹙α-β﹚等于__?

若tanα=3,tanβ=4/3,则tan﹙α-β﹚等于__?
若tanα=3,tanβ=4/3,则tan﹙α-β﹚等于__?

若tanα=3,tanβ=4/3,则tan﹙α-β﹚等于__?
tan﹙α-β﹚
=(tana-tanb)/(1+tanatanb)
=(3-4/3)/(1+3*4/3)
=1/3

tan(a-b)=[tana-tanb]/[1+tanatanb]=1/3


tan﹙α-β﹚
=(tanα-tanβ)/(1+tanαtanβ)
=(3-4/3)/[1+3*(4/3)]
分子分母同乘以3
=(9-4)/(3+12)
=5/15
=1/3

因为tanα=3,tanβ=4/3,所以
tan(α-β)
=(tanα-tanβ)/(1+tanαtanβ)
=(3-4/3)/(1+3×4/3)
=1/3

tan﹙α-β﹚
=(tana-tanb)/(1+tana*tanb)
=(3-4/3)/(1+3*4/3)
=5/3/5
=1/3

tan(α-β)=(tanα-tanβ)/(1+tanαtanβ)=(3-4/3)/(1+3×4/3)=1/3
公式书上都有

tan(α-β)=(tanα-tanβ)/(1+tanαtanβ)=(3-4/3)/(1+3*4/3)=1/3