若tan(π/4-α)=3则tan2α等于

若tan(π/4-α)=3则tan2α等于
若tan(π/4-α)=3则tan2α等于

若tan(π/4-α)=3则tan2α等于
解由tan(π/4-α)=3
得(tanπ/4-tanα)/(1+tanπ/4tanα）=3
即(1-tanα)/(1+tanα）=3
即1-tana=3+3tana
即4tana=-2
即tana=-1/2
即tan2α
=2tana/(1-tan^2a)
=2×（-1/2)/[1-(-1/2)^2]
=-1/(3/4)
=-4/3