Question

The value of $\frac{\tan x}{\tan 3x}$when ever defined never lie between

• A. $\frac{1}{3}$and 3
• B. $\frac{1}{4}$ and 4
• C. $\frac{1}{5}$ and 5
• D. 5 and 6

Answer 1

Answer: (A)

$\frac{1}{3}$and 3

Answer 2

Let, $y = \frac{\tan x}{\tan 3x} = \frac{\tan x}{\frac{3\tan x - \tan^{3}x}{1 - 3\tan^{2}x}}$

$y = \frac{1 - 3\tan^{2}x}{3 - \tan^{2}x} = \frac{\frac{1}{3} - \tan^{2}x}{1 - \frac{1}{3}\tan^{2}x}$

Hence, y should never lie between $\frac{1}{3}$ and 3 whenever defined