Mathematics - Application of Derivative Question with Solution | TestHub

$x=\frac{3-\cos 4\theta +4\sin 2\theta }{2}$ $=\frac{3-\left(1-{\sin }^{2}2\theta \right)+4\sin 2\theta }{2}=(1+\sin 2\theta {)}^2$ $y=\frac{3-\cos 4\theta -4\sin 2\theta }{2}$ $=\frac{3-\left(1-{\sin }^{2}2\theta \right)+4\sin 2\theta }{2}=(1-\sin 2\theta {)}^2$ $\therefore xy={\left(1-{\sin }^{2}2\theta \right)}^2={\cos }^{4}2\theta \le 1$