NCERT Class 12 · Ch 5 Exercise 5.7 · Q12
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.7 Question 12
For y=cos⁻¹x, express y″ in terms of y alone.
💡 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: y″=−cos y/sin³y, −1<x<1 (0<y<π).
- y′=−(1−x²)^(−1/2), so y″=−x/(1−x²)^(3/2).
- Since x=cos y and sin y>0 on (0,π), √(1−x²)=sin y. Substitute to obtain −cos y/sin³y.
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