Mathematics - Inverse Trigonometric Function Question with Solution | TestHub

$$\begin{array}{rl}& {\cos }^{-1}x-{\cos }^{-1}\frac{y}{2}=\alpha \\ & {\cos }^{-1}\left(\frac{xy}{2}+\sqrt{\left(-x^2\right)\left(1-\frac{y^2}{4}\right)}\right)=\alpha \\ & {\cos }^{-1}\left(\frac{xy+\sqrt{4-y^2-4x^2+x^2{y}^2}}{2}\right)=\alpha \\ & \Rightarrow 4-y^2-4x^2+x^2{y}^2=4{\cos }^2\alpha +x^2{y}^2-4xy\cos \alpha \\ & \Rightarrow 4x^2+y^2-4xy\cos \alpha =4{\sin }^2\alpha \end{array}$$