ĐKXĐ: sin2x khác 0
Ta có: tanx + mcotx = 8
<=> sinx/cosx + mcosx/sinx = 8
<=> sin^2x + mcos^2x = 8sinx.cosx
<=> (1 - cos2x)/2 + m.(1 + cos2x)/2 = 4sin2x
<=> 1 - cos2x + m(1 + cos2x) = 8sin2x
<=> (m + 1) + (m - 1)cos2x = 8sin2x
<=> 8sin2x + (1 - m)cos2x = m + 1
PT có nghiệm <=> 8^2 + (1 - m)^2 > (m + 1)^2
<=> 64 + 1 - 2m + m^2 > m^2 + 2m + 1
<=> 64 > 4m
<=> m < 16