A) \[{{\sin }^{-1}}y-{{\sin }^{-1}}x=c\]
B) \[{{\sin }^{-1}}y{{\sin }^{-1}}x=c\]
C) \[{{\sin }^{-1}}(xy)=2\]
D) None of these
Correct Answer: A
Solution :
[a] \[\frac{dy}{dx}=\sqrt{\frac{1-{{y}^{2}}}{1-{{x}^{2}}}}\therefore \frac{dy}{\sqrt{1-{{y}^{2}}}}=\frac{dx}{\sqrt{1-{{x}^{2}}}}\] \[\Rightarrow \int{\frac{dy}{\sqrt{1-{{y}^{2}}}}=\int{\frac{dx}{\sqrt{1-{{x}^{2}}}}}\Rightarrow {{\sin }^{-1}}y={{\sin }^{-1}}x+c}\] \[\therefore {{\sin }^{-1}}y-{{\sin }^{-1}}x=c\]
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