Is the equality correct?

[DimaMazin]

(6^1/2 - 2^1/2)/4 = (2 - 3^1/2)^1/2/2

I have taken sin * cos=1/4 then I have got sine=(2 - 3^1/2)^1/2/2 or (2 + 3^1/2)^1/2/2

Calculator has shown arcsin=15 degrees  but sine 15 degrees=(6^1/2 - 2^1/2)/4

I don't understand how they are connected.

[Ghideon]

1 hour ago, DimaMazin said:

(6^1/2 - 2^1/2)/4 = (2 - 3^1/2)^1/2/2

Hope this helps: yes the equality holds; quick check using Wolfram alpha gives that

 is equal to 

reference: https://www.wolframalpha.com/input/?i=(6^0.5-2^0.5)%2F4

 

 

1 hour ago, DimaMazin said:

sin * cos=1/4

Not sure what that means

[DimaMazin]

21 hours ago, Ghideon said:

Hope this helps: yes the equality holds; quick check using Wolfram alpha gives that

 is equal to 

reference: https://www.wolframalpha.com/input/?i=(6^0.5-2^0.5)%2F4

 

 

Not sure what that means

For example one circular sector of unit circle has area a/2, other circular sector has area Pi/4 - a/2

then   a/2=sin(a)*cosin(a)/2 +(area of circular segment of angle 2a)/2

and     Pi/4 - a/2 = sin(a)*cosin(a)/2+(area of circular segment of angle Pi - 2a)/2

Then area of the twq equal triangles is sin*cosin

[Bufofrog]

46 minutes ago, DimaMazin said:

For example one circular sector of unit circle has area a/2,

So the area in question is 1/2 of the circle?  

48 minutes ago, DimaMazin said:

other circular sector has area Pi/4 - a/2

So that would mean that Pi/4 is the total area 'a'.  Since Pi r^2 = area of a circle, Pi r^2 = Pi/4 or r = 0.5.

Is that correct?  Or are these areas small circles in the larger circle?

[DimaMazin]

7 hours ago, Bufofrog said:

So the area in question is 1/2 of the circle?  

So that would mean that Pi/4 is the total area 'a'.  Since Pi r^2 = area of a circle, Pi r^2 = Pi/4 or r = 0.5.

Is that correct?  Or are these areas small circles in the larger circle?

Unit circle has r=1.

a is angle in radians. You have confused in your inattentiveness .

(6^1/2 - 2^1/2)/4 = (2-3^1/2)^1/2/2

2^1/2(3^1/2-1)/2=(2-3^1/2)^1/2

(3^1/2-1)²/2=2-3^1/2

3-2*3^1/2+1=4-2*3^1/2

[Bufofrog]

10 hours ago, DimaMazin said:

For example one circular sector of unit circle has area a/2, other circular sector has area Pi/4 - a/2

What do you mean by a sector?  The area of a quadrant of the unit circle is Pi/4 and the area of the unit circle is Pi.  What are these 2 sectors and why the relationship between the 2?

[DimaMazin]

3 hours ago, Bufofrog said:

What do you mean by a sector?  The area of a quadrant of the unit circle is Pi/4 and the area of the unit circle is Pi.  What are these 2 sectors and why the relationship between the 2?

https://en.wikipedia.org/wiki/Circular_sector

When sin*cosin=1/4 then area of the one sector is Pi/24 and area of second sector is 5Pi/24