NCERT Class 12 · Ch 5 Miscellaneous Exercise · Q6
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Miscellaneous Exercise Question 6
Differentiate cot⁻¹[(√(1+sin x)+√(1−sin x))/(√(1+sin x)−√(1−sin x))], 0<x<π/2.
💡 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: 1/2.
- On this interval √(1+sin x)=cos(x/2)+sin(x/2), and √(1−sin x)=cos(x/2)−sin(x/2).
- The quotient is cot(x/2). Since x/2∈(0,π/4), principal cot⁻¹ returns x/2. Differentiate to obtain 1/2.
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