NCERT Class 12 · Ch 6 Exercise 6.2 · Q16
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.2 Question 16
Prove log(sin x) increases on (0,π/2) and decreases on (π/2,π).
💡 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: The stated intervals hold.
- Since sin x>0 on (0,π), this logarithm is defined. Its derivative is cot x.
- Cotangent is positive in the first interval and negative in the second.
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