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x+y=pi/2; sin^2x-sin^2y=1

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The solution

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        pi
x + y = --
        2 
$$x + y = \frac{\pi}{2}$$
   2         2       
sin (x) - sin (y) = 1
$$\sin^{2}{\left(x \right)} - \sin^{2}{\left(y \right)} = 1$$
sin(x)^2 - sin(y)^2 = 1
Rapid solution
$$x_{1} = \frac{\pi}{2}$$
=
$$\frac{\pi}{2}$$
=
1.57079632679490

$$y_{1} = 0$$
=
$$0$$
=
0