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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 cot^ - 1 ((n)/(2π)) > (2π)/(3) , then the maximum value of the...

If cot−1(n2π)>2π3cot^{- 1}\left(\dfrac{n}{2\pi}\right) > \dfrac{2\pi}{3}, then the maximum value of the integer nn is

Options

  1. A33
  2. B44
  3. C−4- 4
  4. D−3- 3

Correct answer

C. −4- 4

Step-by-step solution

We have, 2π3<cot−1(n2π)<π⇒cot2π3>n2π>−∞\dfrac{2\pi}{3} < cot^{- 1}\left(\dfrac{n}{2\pi}\right) < \pi ⇒ cot\dfrac{2\pi}{3} > \dfrac{n}{2\pi} > - \infty
⇒−13>n2π>−∞⇒−2π3>n>−∞⇒ - \dfrac{1}{\sqrt{3}} > \dfrac{n}{2\pi} > - \infty ⇒ - \dfrac{2\pi}{\sqrt{3}} > n > - \infty
Maximum value of nn is −4- 4
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