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Discuss the Continuity of the Cosine, Cosecant, Secant and Cotangent Functions, - CBSE (Commerce) Class 12 - Mathematics

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Question

Discuss the continuity of the cosine, cosecant, secant and cotangent functions,

Solution

It is known that if and are two continuous functions, then

It has to be proved first that g (x) = sin and h (x) = cos x are continuous functions.

Let (x) = sin x

It is evident that g (x) = sin x is defined for every real number.

Let be a real number. Put x = c + h

If x → c, then h → 0

Therefore, g is a continuous function.

Let h (x) = cos x

It is evident that h (x) = cos x is defined for every real number.

Let be a real number. Put x = c + h

If x ® c, then h ® 0

(c) = cos c

Therefore, h (x) = cos x is continuous function.

It can be concluded that,

Therefore, cotangent is continuous except at np, Î Z

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 5: Continuity and Differentiability
Q: 22 | Page no. 160
Solution Discuss the Continuity of the Cosine, Cosecant, Secant and Cotangent Functions, Concept: Algebra of Continuous Functions.
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