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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NTA Abhyas 2020 · Mathematics · Inverse Trigonometric Functions

If ^ - 1 (x)/(π) ≤ (π)/(6), then the maximum value of 3 x is (Use π...

If tan⁡−1xπ≤π6,\tan^{- 1} \dfrac{x}{\pi} \le \dfrac{\pi}{6}, then the maximum value of 3x\sqrt{3}x is (Useπ=3.14\pi = 3 . 14)

Correct answer

3.14

Step-by-step solution

We have tan⁡−1xπ≤π6\tan^{- 1} \dfrac{x}{\pi} \le \dfrac{\pi}{6}
⇒tan⁡(tan⁡−1xπ)≤tanπ6⇒ \tan \left(\tan^{- 1} \dfrac{x}{\pi}\right) \le tan \dfrac{\pi}{6}
⇒xπ≤13⇒x≤π3⇒ \dfrac{x}{\pi} \le \dfrac{1}{\sqrt{3}} ⇒ x \le \dfrac{\pi}{\sqrt{3}}
∴∴ the maximum value of 3x\sqrt{3}x is π\pi
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