![Ex 5.1, 22 (iv) - Chapter 5 Class 12 Continuity and Differentiability - Part 2](https://d1avenlh0i1xmr.cloudfront.net/3fba15b7-d35a-47ff-9b4b-4606d41023a4/slide9.jpg)
Ex 5.1
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