Let's fistly consider what is sectorsgenta then the hypothesis

[math]\frac{xy}{2}=\frac{1}{\sin 2 \alpha}[/math]

Edited yesterday at 11:12 AM1 day by Genady

2 hours ago, Genady said:

xy2=1sin2α

I have mistaken because it correct only when à=Pi/4 .

You are correct only in the case too. Because green line is not tangenta to the circle in point [cos(a); sin(a)] . It is tangenta in other point.

xy/2 is the area of triangle oxy

This area depends upon the radius of the circle.

So no in general xy/2 is not equal to 1.

According to the drawing, the radius of the circle is 1.

2 hours ago, DimaMazin said:

I have mistaken because it correct only when à=Pi/4 .

You are correct only in the case too. Because green line is not tangenta to the circle in point [cos(a); sin(a)] . It is tangenta in other point.

You should've asked me, what is [math]\alpha[/math].

It is an angle between the green line and the axis.

1 hour ago, Genady said:

According to the drawing, the radius of the circle is 1.

You should've asked me, what is α.

It is an angle between the green line and the axis.

a is arc of unit circle in radians. It shown on diagram.

27 minutes ago, DimaMazin said:

a is arc of unit circle in radians. It shown on diagram.

OK, then [math]\frac{xy}{2}=\frac{1}{\sin 2\beta}[/math].

55 minutes ago, DimaMazin said:

a is arc of unit circle in radians. It shown on diagram.

Well even with the crick in my neck I can see that you have mislabled the second digram.