已知α∈(-π/2,0),sinα=-4/5,则tan(α+π/4)=
问题描述：
已知α∈(-π/2,0),sinα=-4/5,则tan(α+π/4)=
答
α∈(-π/2,0)
则cosα>0
∵ cos²α=1-sin²α=1-16/25=9/25
∴ cosα=3/5
∴ tanα=sinα/cosα=-4/3
∴ tan(α+π/4)
=[tanα+tan(π/4)]/[1-tanαtan(π/4)]
=(tanα+1)/(1-tanα)
=(-4/3+1)/(1+4/3)
=(-1/3)/(7/3)
=-1/7