COMEDK · Maths · 26. Differentiation
If \(y=\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2\), then \(\left(1-x^2\right) \dfrac{d^2 y}{d x^2}-x \dfrac{d y}{d x}=\)
- A 4
- B 2
- C 0
- D 3
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
Given \(y = (\sin^{-1} x)^2 + (\cos^{-1} x)^2\). Using the identity \(\cos^{-1} x = \dfrac{\pi}{2} - \sin^{-1} x\), we have \(y = (\sin^{-1} x)^2 + (\dfrac{\pi}{2} - \sin^{-1} x)^2\). Let \(u = \sin^{-1} x\). Then…
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