设tan(α+β)=2/3,tan(β-π/4)=1/4.则(1+tanα)/(1-tanα)的值为

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设tan(α+β)=2/3,tan(β-π/4)=1/4.则(1+tanα)/(1-tanα)的值为

设tan(α+β)=2/3,tan(β-π/4)=1/4.则(1+tanα)/(1-tanα)的值为
设tan(α+β)=2/3,tan(β-π/4)=1/4.则(1+tanα)/(1-tanα)的值为

设tan(α+β)=2/3,tan(β-π/4)=1/4.则(1+tanα)/(1-tanα)的值为
(1+tanα)/(1-tanα)
= [tan(π/4)+tanα]/[1-tan(π/4)tanα]
= tan(π/4+α)
= tan[(α+β)-(β-π/4)]
=[ tan(α+β)-tan(β-π/4)]/[1+ tan(α+β)tan(β-π/4)]
= (2/3-1/4)/[1+(2/3)*(1/4)]
=(5/12)/[1+2/12]
=5/14

tan(α+π/4)=tan(α+β-β+π/4)=(tan(α+β)-tan(β-π/4))/(1+tan(α+β)*tan(β-π/4))
=(2/3-1/4)/(1+2/3*1/4)=5/14
(1+tanα)/(1-tanα)=(tan(π/4)+tanα)/(1-tanαtan(π/4))=tan(α+π/4)=5/14