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Prove that (tan x)/(tan 3 x) never lies ...

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

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To prove that \(\frac{\tan x}{\tan 3x}\) never lies between \(\frac{1}{3}\) and \(3\), we can follow these steps: ### Step 1: Define the variable Let \(y = \frac{\tan x}{\tan 3x}\). ### Step 2: Use the identity for \(\tan 3x\) Using the trigonometric identity for \(\tan 3x\): \[ ...
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