AP EAMCET · Maths · Differentiation
If \(\cos ^{-1}\left(\frac{x^2-y^2}{x^2+y^2}\right)=\sin ^{-1}(a)\) then \(\frac{d y}{d x}\) is equal to
- A \(y / x\)
- B \(-y / x\)
- C \(x / y\)
- D \(-x / y\)
Answer & Solution
Correct Answer
(A) \(y / x\)
Step-by-step Solution
Detailed explanation
Given, \(\cos ^{-1}\left(\frac{x^2-y^2}{x^2+y^2}\right)=\sin ^{-1} a\) \[ \Rightarrow \quad \frac{x^2-y^2}{x^2+y^2}=\cos \left(\sin ^{-1} a\right)=c \] On applying componendo and dividendo law, we get…
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