CUET · MATHS · PYQ PAPER 2025
If \(x=a \sec ^3 \theta, y=a \tan ^3 \theta\) then \(\frac{d^2 y}{d x^2}\) equals.
- A \(\frac{\cos ^5 \theta}{3 a \sin \theta}\)
- B \(\frac{3 a \cos ^5 \theta}{\sin \theta}\)
- C \(\frac{\sin ^5 \theta}{3 a \cos \theta}\)
- D \(\frac{3 a \sin ^5 \theta}{\cos \theta}\)
Answer & Solution
Correct Answer
(A) \(\frac{\cos ^5 \theta}{3 a \sin \theta}\)
Step-by-step Solution
Detailed explanation
\(\frac{dx}{d\theta} = 3a \sec^2 \theta (\sec \theta \tan \theta) = 3a \sec^3 \theta \tan \theta\) \(\frac{dy}{d\theta} = 3a \tan^2 \theta \sec^2 \theta\)…
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