Mathematics - Trigonometric Equation Question with Solution | TestHub

$\frac{{\sin }^2\mathrm{x}+\frac{1}{{\mathrm{x}}^2}}{2\frac{\sin \mathrm{x}}{\mathrm{x}}}={\sin }^2\mathrm{y}$

LHS $\ge 1$ and RHS $\le 1.\Rightarrow {\sin }^{2}y=1\Rightarrow \sin y=\pm 1\Rightarrow y=\frac{\pi }{2},\frac{3\pi }{2}$

And ${\sin }^{2}x=\frac{1}{x^2}$

There are four values of x satisfying equation [1] ∴ ordered pairs $=8$