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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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