If $$tan$$−$$1$$⁡xπ<π$$3$$, x∈N then the maximum value of x, is

We have, $$tan$$−$$1$$⁡$$x3$$<π$$3=$$ $$tan$$−$$1$$⁡$$x3$$

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If $\tan^{- 1} \frac{x}{π} < \frac{π}{3}, x \in N$ then the maximum value of $x,$ is

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Solution

We have,
$\begin{array}{l} t {an}^{- 1} \frac{x}{3} < \frac{π}{3} \\ = \tan^{- 1} \frac{x}{3} < \tan^{- 1} \sqrt{3} \Rightarrow \frac{x}{3} < \sqrt{3} \Rightarrow x < 3 \sqrt{3} \end{array}$
Hence, the greatest integer value of $x$ is $5 .$

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