If x + y = 90, simplify (sinx + siny)2−2sinxsiny

If $x+y=90$
Solve for $(\sin x+\sin y{)}^2-2\sin x\sin y$
$x+y=90$ ---(1)
$(\sin x+\sin y{)}^2-2\sin x\sin y$ ----(2)
$x=90-y$ ---(3)
Expanding eqn (2)
Therefore: ${\sin }^{2}x+{\sin }^{2}y+2\sin x\sin y-2\sin x\sin y$
=> ${\sin }^{2}x+{\sin }^{2}y$ --- (4)
Substitute the value of $x$ in eqn (3) into eqn (4)
=> ${\sin }^2(90-y)+{\sin }^{2}y$ ---(5)
Expanding eqn (5)
=> ${\sin }^2\left(90\right)-{\sin }^{2}y+{\sin }^{2}y$
=> ${\sin }^2\left(90\right)+0$
=> ${\sin }^2\left(90\right)$
=> $\left(\sin \right(90){)}^2$
=> $1^2$
= $1$