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Maths Inverse Trigonometric Functions Inverse Trigonometric Functions, Inverse Trigo Identities Numeric Response

Published by: CGP EDU Academic Team

Published on: August 12, 2026

If cot –1 > , n ∈ N, then find the minimum value of n.

Text Solution

Verified by Experts

The correct answer is:

(3)

We have, cot –1 >

⇒ < cot

{as cot x is decreasing for 0 < x < π }

⇒ n 2 – 10n + 21. 6 < π

⇒ n 2 – 10 n + 25 + 21.6 – 25 < π

⇒ (n –5) 2 < π + 3.4

⇒ – < n – 5 <

⇒ 5 – < n < 5 + …(i)

Since, π = 5.5 nearly

∴ ~ ~ 2.9

⇒ 2. 1 < n < 7.9

∴ n = 3, 4, 5, 6, 7 {as n ∈ N}

or minimum value of n = 3

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