Prove that cotangent function is continous [with Video] - Teachoo

Ex 5.1, 22 (iv) - Chapter 5 Class 12 Continuity and Differentiability - Part 2


Ex 5.1, 22 (iv) Discuss the continuity of cotangent functions.Let 𝒇(𝒙) = 𝒄𝒐𝒕 𝒙 𝑓(π‘₯) = cos⁑π‘₯/sin⁑π‘₯ 𝑓(π‘₯) is defined for all real number except where sin⁑π‘₯ = 0 i.e. x = 𝒏𝝅 Let 𝒑(𝒙)=cos⁑π‘₯ & 𝒒(𝒙)=sin⁑π‘₯ We know that sin⁑π‘₯ & cos x is continuous for all real number ∴ p(x) & q (x) are continuous functions By Algebra of continuous function If 𝑝, π‘ž are continuous , then 𝒑/𝒒 is continuous. Thus, 𝑓(π‘₯) = cos⁑π‘₯/sin⁑π‘₯ is continuous for all real numbers except where sin⁑π‘₯ = 0 i.e. 𝒙= 𝒏𝝅, π’βˆˆπ’ So, 𝒄𝒐𝒕 𝒙 is continuous at all real numbers except where 𝒙= 𝒏𝝅, π’βˆˆπ’

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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.