若cos2α=m 则tan(α+π/4)=
问题描述：
若cos2α=m 则tan(α+π/4)=
RT
答
∵cos2α=2cosα^2-1=m
∴cosα=√[(1+m)/2]
∴tanα=√[(1-m)/(1+m)]
∴tan(π/4+α)=(tanπ/4+tanα)/(1-tanπ/4tanα)
=(1+tana)/(1-tana)
=[1+√(1-m^2)]/m