jasperE3 wrote: Find all pairs of real numbers $(x,y)$ satisfying the equation $$\sin^2x+\sin^2y=\frac{|x|}x+\frac{|y|}y.$$ We have $xy\ne 0$ and : Either $x,y<0$ and $\sin^2x+\sin^2y=-2$, impossible Either $xy<0$ and $\sin^2x+\sin^2y=0$ and so $\boxed{(x,y)=(m\pi,n\pi)\text{ where m,n are any integers such that }mn<0}$ Either $x,y>0$ and $\sin^2x+\sin^2y=2$ and so $\boxed{(x,y)=(\frac{\pi}2+m\pi,\frac{\pi}2+n\pi)\text{ where m,n are any nonnegative integers}}$.