Mathematics - Trigonometric Equation Question with Solution | TestHub

$\sqrt{{\sin }^{2}x-\sin x+\frac{1}{2}}=\sqrt{{\left(\sin x-\frac{1}{2}\right)}^2+\frac{1}{4}}\ge \frac{1}{2}$ and

$\left({\sec }^{2}y\right)\ge 1,2^{{\sec }^{2}y}\ge 2$

It is possible only when $\sin x=\frac{1}{2},{\sec }^{2}y=1$

$\therefore x=\frac{\pi }{6},\frac{5\pi }{6},\frac{13\pi }{6},\frac{17\pi }{6}$

$y=0,\pi ,2\pi ,3\pi$

No. of ordered pairs $=16$