NCERT Class 12 · Ch 5 Exercise 5.1 · Q22
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.1 Question 22
Discuss continuity of cosine, cosecant, secant and cotangent.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: cos: R; cosec and cot: R∖{nπ}; sec: R∖{π/2+nπ}, n∈Z.
- Cosine is continuous on all of R. Reciprocals and quotients preserve continuity where denominators do not vanish.
- For cosec and cot the denominator is sin x, zero at nπ. For sec it is cos x, zero at π/2+nπ. These excluded points are poles.
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