若tan(α+π/4)=-3/5,求tan(α-π/4)的值

问题描述:

若tan(α+π/4)=-3/5,求tan(α-π/4)的值

tan(α-π/4)=tan(α+π/4-π/2)=-cot(α+π/4)=5/3

tan(α+π/4)
=(tana+1)/(1-tana)=-3/5
得 3tana-3=5tana+5
得2tana=-8 即tana=-4
所以tan(α-π/4)=(tana-1)/(1+tana)=-5/(1-4)=5/3

tan(α+π/4)=-3/5
(tanα+1)/(1-tanα)=-3/5
tanα=-4
tan(α-π/4)=(tanα-1)/(1+tanα)=5/3
tan(α-π/4)=-cot(α-π/4+π/2)=-cot(α+π/4)=-1/tan(α+π/4)=5/3

tan(α-π/4)=tan(α+π/4-π/2)=-ctan(α+π/4)=5/3