NCERT Class 12 · Ch 5 Exercise 5.6 · Q11
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.6 Question 11
If x=√(a^(sin⁻¹t)), y=√(a^(cos⁻¹t)), show dy/dx=−y/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: dy/dx=−y/x, for a>0, a≠1 and −1<t<1.
- Write x=exp[(log a)sin⁻¹t/2], y=exp[(log a)cos⁻¹t/2].
- Then x′=x log a/(2√(1−t²)), y′=−y log a/(2√(1−t²)).
- Taking the ratio gives −y/x. The restrictions make the real powers and nonzero quotient valid. At a=1 the parametrisation is the constant point (1,1), so this derivative cannot be inferred.
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