∵α∈[-π/4,3π/4],
∴α-π/4∈[-π/2,π/2]
∵sin(α-π/4)=-√5/5
∴cos(α-π/4)=2√5/5
∴tan(α-π/4)=-1/2
展开左边(tanα-1)/(1+tanα)=-1/2
解得tanα=1/3