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Unsolved Challenge cos(π/7)

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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,587
Prove that $\cos\dfrac{\pi}{7}=\dfrac{1}{6}+\dfrac{\sqrt{7}}{6}\left(\cos\left(\dfrac{1}{3}\arccos\dfrac{1}{2\sqrt{7}}\right)+\sqrt{3}\left(\dfrac{1}{3}\cos\dfrac{1}{2\sqrt{7}}\right)\right)$.