If c o t - 1 n 2 π > 2 π 3 , then the maximum value of the integer n is

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Question: Answered & Verified by Expert

If

c o t^{- 1} (\frac{n}{2 π}) > \frac{2 π}{3}

, then the maximum value of the integer

n

is

MathematicsInverse Trigonometric FunctionsJEE Main

Options:

A $3$
B $4$
C $- 4$
D $- 3$

Solution:

2386 Upvotes Verified Answer

The correct answer is:

- 4

We have,

\frac{2 π}{3} < c o t^{- 1} (\frac{n}{2 π}) < π \Rightarrow c o t \frac{2 π}{3} > \frac{n}{2 π} > - \infty

\Rightarrow - \frac{1}{\sqrt{3}} > \frac{n}{2 π} > - \infty \Rightarrow - \frac{2 π}{\sqrt{3}} > n > - \infty

Maximum value of

n

is

- 4

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