The function f (x) = cot x is discontinuous on the set

(A) {x=nπ:n∈ Z}                

(B) {x=2nπ:n∈ Z}  

(C) {x= (2n+1)  π/2   ; n ∈z}                      

(D) {x= n π/2   ; n ∈z}

This question is similar to Example 18 - Chapter 5 Class 12 - Continuity and Differentiability

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Question 14 The function f (x) = cot x is discontinuous on the set (A) {๐‘ฅ=๐‘›๐œ‹:๐‘›โˆˆ๐’} (B) {๐‘ฅ=2๐‘›๐œ‹:๐‘›โˆˆ๐’} (C) {๐‘ฅ=(๐Ÿ๐’+๐Ÿ) ๐…/๐Ÿ ;๐‘›โˆˆ๐’›} (D) {๐‘ฅ=๐’๐…/๐Ÿ ;๐‘›โˆˆ๐’›} Let ๐‘“(๐‘ฅ) = c๐‘œ๐‘กโก๐‘ฅ ๐’‡(๐’™) = ๐’„๐’๐’”โก๐’™/๐’”๐’Š๐’โก๐’™ Here, ๐‘“(๐‘ฅ) is defined for all real number except ๐’”๐’Š๐’โก๐’™ = 0 i.e. for all x except x = ๐’๐… Thus, cotโก๐‘ฅ is discontinuous on the set {๐’™=๐’๐…:๐’โˆˆ๐’} So, the correct answer is (A)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.