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

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Ex 5.1, 22 (iii) Discuss the continuity of the cosine, cosecant, secant and cotangent functions. Let 𝒇(𝒙)="sec x" 𝑓(𝑥) = 1/c𝑜𝑠⁡𝑥 Let 𝒑(𝒙)=1 & 𝒒(𝒙)=𝑐𝑜𝑠⁡𝑥 Since, p(x) is a constant, ∴ 𝑝(𝑥) is continuous We know that cos⁡𝑥 is continuous for all real number ∴ 𝑞(𝑥) is continuous By Algebra of continuous function If 𝑝, 𝑞 are continuous , then 𝒑/𝒒 is continuous. Thus, 𝑓(𝑥) = 1/cos⁡𝑥 is continuous for all real numbers except points where cos⁡𝑥 = 0 i.e. 𝒙=(𝟐𝒏+𝟏) 𝝅/𝟐, 𝑛∈𝒁 So, 𝒔𝒆𝒄 𝒙 is continuous at all real numbers except where 𝒙=(𝟐𝒏+𝟏) 𝝅/𝟐, 𝒏∈𝒁

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Davneet Singh

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.