NCERT Class 12 · Ch 9 Exercise 9.3 · Q1
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 1
Solve y′=(1−cos x)/(1+cos x).
💡 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: \(x + y - 2 \tan{\left(\frac{x}{2} \right)}\) = C.
- Use (1−cos x)/(1+cos x)=tan²(x/2)=sec²(x/2)−1.
- Integrating gives y=2tan(x/2)−x+C; work away from odd multiples of π.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
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