Question

已知tan2α=3/4 ,α属于(0,π/4),sina+cosα/sina-cosα=

Answer 1

tan2α=2tanα/(1-tan²α)

∴ 3/4=2tanα/(1-tan²α)

∴ 3-3tan²α=8tanα

∴ 3tan²α+8tanα-3=0

即 (tanα+3)(3tanα-1)=0

∴ tanα=-3或tanα=1/3

∵ α是锐角

∴ tanα=1/3

∴ (sinα+cosα)/(sinα-cosα)

=(tanα+1)/(tanα-1) 分子分母同时除以cosα得到

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

=(4/3)/(-2/3)

=-2