Is cosecant function continuous? [with Video] - Teachoo - Ex 5.1

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

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Ex 5.1, 22 (ii) Discuss the continuity of the cosine, cosecant, secant and cotangent functions.Let 𝒇(𝒙)="cosec (x)" 𝑓(π‘₯) = 1/sin⁑π‘₯ Let 𝒑(𝒙)=1 & 𝒒(𝒙)=sin⁑π‘₯ Since, p(x) is a constant, ∴ 𝑝(π‘₯) is continuous. We know that sin⁑π‘₯ is continuous for all real numbers ∴ π‘ž(π‘₯) is continuous. By Algebra of continuous function If 𝑝, π‘ž are continuous , then 𝒑/𝒒 is continuous. Thus, 𝑓(π‘₯) = 1/sin⁑π‘₯ is continuous for all real numbers except points where sin⁑π‘₯ = 0 i.e. 𝒙= 𝒏𝝅, π’βˆˆπ’ So, 𝒄𝒐𝒔𝒆𝒄 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.