Mathematics - Differential Equation Question with Solution | TestHub

Put $x=\sin \theta$ and $y=\sin \varphi$ $\Rightarrow \cos \theta +\cos \varphi =a(\sin \theta -\sin \varphi )$ $\Rightarrow 2\cos$ $\begin{array}{rl}& \frac{\theta +\varphi }{2}\cos \frac{\theta -\varphi }{2}=2a\cos \frac{\theta +\varphi }{2}\sin \frac{\theta -\varphi }{2}\\ \Rightarrow \cot \frac{\theta -\varphi }{2}=a\Rightarrow \theta -\varphi =2{\cot }^{-1}\mathrm{a}& \\ \Rightarrow {\sin }^{-1}\mathrm{x}-{\sin }^{-1}\mathrm{y}=2{\cot }^{-1}\mathrm{a}& \\ \text{ Differentiate }\frac{1}{\sqrt{1-{\mathrm{x}}^2}}-\frac{1}{\sqrt{1-{\mathrm{y}}^2}}\frac{\mathrm{dy}}{\mathrm{dx}}=0& \end{array}$ so the degree is one