Question

已知cosα=-4/5,且α属于(π/2,π),则tan(π/4-α)等于?

Answer 1

cosα=-4/5,

α属于(π/2,π),

∴ sinα>0

∴ sinα=√(1-cos²α)=√(1-16/25)=3/5

∴ tanα=sinα/cosα=(3/5)/(-4/5)=-3/4

∴ tan(π/4-α)

=[tan(π/4)-tanα]/[1+tan(π/4)tanα]

=(1-tanα)/(1+tanα)

=(1+3/4)/(1-3/4)

=7