In the first, top rated, comment on the original post linked below, the author wrote the function r=cos(x)1−cos(x). I do not understand how they got to this equation. I get how they solved for x in their first step. Can you please explain how they solved for r.
This is the picture of the problem, where we are solving for r, given x=n−22n
Original Post
Numbers of circles around a circle
Answer
In the right Triangle, we can write cosx as
Base divided by the hypotenuse
cosx=rr+1
1cosx=1+1r
1r=1cosx−1
1r=1−cosxcosx
r=cosx1−cosx
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