Question

已知tan（（π/4）+α）=1/2,求tan2α的值,（sin2α-cos²α）/（1+cos2α）的值

Answer 1

∵tan(π/4 α)=(tanπ/4 tanα)/(1-tanπ/4*tanα)=(1 tanα)/(1-tanα)=-1/2

∴tanα=-3

∴sinα/cosα=tanα=-3,即sinα=-3cosα

代入sin²α cos²α=1,解得sin²α=9/10,cos²α=1/10

又∵sinα/cosα=-3