Provide a complete proof for the statement: prove that $\underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\dots+\sqrt{2}}}}}_{\text{n radicals}}=2\cos{\frac{\pi}{2^{n+1}}}$
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I haven't attempted the problem myself yet, but think "half-angle formula." – Charles Hudgins Jun 12 '21 at 01:56
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see https://en.wikipedia.org/wiki/Viète%27s_formula – Jun 12 '21 at 04:03