TS EAMCET · Maths · Differentiation
If \(\sqrt{1-x^2}+\sqrt{1-y^2}=a(x-y)\), then \(\left[\left(1-x^2\right)^2 \frac{d^2 y}{d x^2}+y\left(1-x^2\right)\right] \frac{d y}{d x}=\)
- A \(0\)
- B \(x\left(1-y^2\right)\)
- C \(y\left(1-x^2\right)\)
- D \(\sqrt{1-x^2} \sqrt{1-y^2}\)
Answer & Solution
Correct Answer
(B) \(x\left(1-y^2\right)\)
Step-by-step Solution
Detailed explanation
Given, \(\sqrt{1-x^2}+\sqrt{1-y^2}=a(x-y)\) Putting \(x=\sin A\) and \(y=\sin B\), then \(\Rightarrow \quad \sin ^{-1} x-\sin ^{-1} y=2 \cot ^{-1}(a)\) Differentiating w.r.t. \(X\), we get…
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