Trig +Nested Radicals = Fun
Geometry
Level
4
If \(\sqrt{2 + \sqrt{2+\sqrt2}} \) is in the form of \(A \cos \left( \dfrac BC \pi \right) \), where \(A,B\) and \(C\) are positive integers with \(B,C\) coprime, find the minimum value of \(A+B+C\).
Bonus: Investigate why \(\sqrt { 2+\sqrt { 2+\sqrt { 2 \cdots} } } =2\) using trigonometry.
by
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