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Last updated at April 16, 2024 by Teachoo

Ex 5.1, 22 (iv) Discuss the continuity of cotangent functions.Let π(π) = πππ π π(π₯) = cosβ‘π₯/sinβ‘π₯ π(π₯) is defined for all real number except where sinβ‘π₯ = 0 i.e. x = ππ Let π(π)=cosβ‘π₯ & π(π)=sinβ‘π₯ We know that sinβ‘π₯ & cos x is continuous for all real number β΄ p(x) & q (x) are continuous functions By Algebra of continuous function If π, π are continuous , then π/π is continuous. Thus, π(π₯) = cosβ‘π₯/sinβ‘π₯ is continuous for all real numbers except where sinβ‘π₯ = 0 i.e. π= ππ , πβπ So, πππ π is continuous at all real numbers except where π= ππ , πβπ