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Question Number 44623 by mondodotto@gmail.com last updated on 02/Oct/18

$$\mathbf{given}\mathbf{that}{\mathbf{sin}}^{-1}\mathit{x}+{\mathbf{sin}}^{-1}\mathit{y}=\mathbf{c}$$$$\mathbf{show}\mathbf{that}\frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{x}}+\sqrt{\frac{1-{\mathit{y}}^2}{1-{\mathit{x}}^2}}=0$$

Answered by tanmay.chaudhury50@gmail.com last updated on 02/Oct/18

$$\frac{d}{dx}({sin}^{-1}x+{sin}^{-1}y)=\frac{dc}{dx}$$$$\frac{1}{\sqrt{1-x^2}}+\frac{1}{\sqrt{1-y^2}}\frac{dy}{dx}=0$$$$\frac{\sqrt{1-y^2}}{\sqrt{1-x^2}}+\frac{dy}{dx}=0$$

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