CBSE Class 12 Mathematics 2026 Main Paper 65/2/1 · Q222 Marksparametric_derivatives
CBSE Class 12 Mathematics 2026 Main Paper 65/2/1 · Question 22 (Continuity And Differentiability)
If x=a sin³t and y=b cos³t, find dy/dx at t=π/4.
✅ Step-by-Step Solution
Final Answer: −b/a for a≠0.
- Differentiate to get x′=3a sin²t cos t and y′=−3b cos²t sin t.
- At π/4 both sine and cosine are 1/√2, and x′ is nonzero for a≠0.
- The quotient y′/x′ is −b/a.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Differentiate to get x′=3a sin²t cos t and y′=−3b cos²t sin t.
- [1 mark] At π/4 both sine and cosine are 1/√2, and x′ is nonzero for a≠0.
- [0.5 marks] The quotient y′/x′ is −b/a.
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