Function Problem 7

We have $x^2-4x+5-siny=0$ and $x,y>0$ .Then we can write this quadratic equation as:- $x^2-4x+4+1-siny=0$ $\implies(x-2)^2+1=siny$ $\implies(x-2)^2=siny-1$ so we equate it to 0 and hence we get $x=2$ and $y=(4n+1)\dfrac{\pi}{2}$ . We substitute these values in $xy$ and we get $2.\dfrac{\pi}{2}=\pi$