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Q.
If $\tan^{-1} \frac{x}{\pi} < \frac{\pi}{3} , x \in N$, then the maximum value of x is
Inverse Trigonometric Functions
Solution:
We have,
$\tan^{-1} \frac{x}{\pi} < \frac{\pi}{3}\Rightarrow \tan\left(\tan^{-1} \frac{x}{\pi}\right) < \tan \frac{\pi}{3} $
$\Rightarrow \frac{x}{\pi} < \sqrt{3} \Rightarrow x < \sqrt{3} \pi= 5.5 $ (approx.)
$\therefore $ the maximum value of x is 5.