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

We have,$$tan$$−$$1$$⁡xπ<π$$3$$ ⇒$$tan$$⁡$$tan$$−$$1$$⁡xπ

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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,
$\tan^{- 1} \frac{x}{π} < \frac{π}{3} \begin{array}{l} \Rightarrow \tan (\tan^{- 1} \frac{x}{π}) < \tan \frac{π}{3} \\ \Rightarrow \frac{x}{π} < \sqrt{3} \Rightarrow x < \sqrt{3} π = 5.44 \end{array}$
$∴$ The maximum value of x is 5.44

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