NCERT Class 12 · Ch 6 Exercise 6.2 · Q9
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.2 Question 9
Prove 4sin θ/(2+cos θ)−θ is increasing on [0,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: Strictly increasing on [0,π/2].
- The derivative is cos θ(4−cos θ)/(2+cos θ)².
- It is positive for 0≤θ<π/2 and zero at π/2. Continuity at the endpoints and the derivative criterion give strict increase on the whole interval.
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