Question

Prove that tan3x/tanx does not lie between 1/3 and 3

Answer 1

since the value of tanx lies between 0to ∞ then , 0≤tanx<∞. and from the equation it can be seen that tan3x≥0.............(1) =>tan3x/tanx≥0
now 1/3<tanx<3(say)
=>1<tan3x<3=l
but we know that from 1 that tanx≥0.
hence our assumption was wrong.
thus the value of tan3x/tanx does not lie between 1/3 and 3.