Prove that `(tan3x)/(tanx)` never lies between `1/3a n d3` .

Explanation

To prove that \(\frac{\tan 3x}{\tan x}\) never lies between \(\frac{1}{3}\) and \(3\), we will use the formula for \(\tan 3\theta\):

\[ \tan 3\theta = \frac{3\tan \theta - \tan^3 \theta}{1 - 3\tan^2 \theta} \]

Let \(\tan x = t\). Then, substituting \(\theta = x\), we have:

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