You denied what you *see. Case closed.

No, I didn't.

I explained quite clearly why it is the case.

Here is an image for you:

Firstly, it is not to scale.

It is showing an equilateral triangle, which has been cut in half.

Lengths are in red, angles in purple.

Let me know at what you point you disagree with me:

1 - It's (the black triangle) an equilateral triangle (remember, not to scale).

2 - Thus all three angles are the same

3 - Thus a1=a2=a=b1+b2=60 degrees.

4 - It also means all sides are equal.

5 - Thus r1=r2=r=x1+x2

6 - This triangle is cut in half by the grey line.

7 - This means x1=x2=x.

8 - Thus r=2*x

9 - As the smaller triangles have 3 sides each, which are equivalent, i.e. y is common, r1=r2, and x1=x2, these triangles are congruent.

10 - As these triangles are congruent the corresponding angles are equal.

11 - Thus b1=b2=b.

12 - Thus c1=c2=c.

13 - As c1 and c2 make a straight line, c1+c2=2*c=180 degrees

14 - Thus c=90 degrees

15 - Thus a, b, c make a right angle triangle, with angles 60, 30 and 90 respectively with a hypotenuse of 2*x and a side adjacent to the 60 degree angle of x.

16 - Cos(a), refers to the cosine of a, which is the ratio of the side in a right angle triangle adjacent to the angle a and its hypotenuse, i.e. cos(a)=x/r.

17 - thus cos(60 degrees)=x/r=x/2*x=0.5

Which point of these do you disagree with?

It is quite simple reasoning which shows beyond any doubt that your claim is wrong.