`(tanx)/(tan 3x)` wherever defined cannot lie between `1/3 and 3.`

If y=(tanx)/(tan3x), then

tan( 3x +1)

Prove that (tan3x)/(tan x) never lies between (1)/(3) and 3.

Prove that (tan3x)/(tan x) never lies between (1)/(3) and 3

9Prove that the values of the function (sin x cos3x)/(sin3x cos x) cannot lie between (1)/(3) and 3 for any real x

Prove that the values of the function ("sin"xcos3x)/(cosx"sin"3x) do not lie between (1)/(3) and 3

(3x+5)(1+tanx)

Prove that if the equation x^(2)+9y^(2)-4x+3=0 is satisfied for real values of x and y, then x must lie between 1 and 3and y must lie between-1/3and 1/3 .

If tan 3A /tan A =k , show that sin 3A/sin A = 2k/k-1 an and k cannot Second Method lie between 1/3 and 3.