Question

已知cot（45°+α）=2,则（1+sec2α-tan2α）/（1-sec2α+tan2α）=?

Answer 1

cot（45°+α）=2

tan(45+α)=(1+tanα)/(1-tanα)=1/2

1-tanα=2+2tanα

3tanα=-1

tanα=-1/3

（1+sec2α-tan2α）/（1-sec2α+tan2α）

=(cos2α+1-sin2α)/(cos2α-1+sin2α)

=(2cos^2α-2sinαcosα)/(2sinαcosα-2sin^2α)

=(1-tanα)/(tanα-tanα^2)

=(1+1/3)/(-1/3-1/9)

=(4/3)/(-4/9)

=-1/3