Jun 12, 2020 Thread starter Admin #1 anemone MHB POTW Director Staff member Feb 14, 2012 3,587 Prove that $\cos\dfrac{\pi}{7}=\dfrac{1}{6}+\dfrac{\sqrt{7}}{6}\left(\cos\left(\dfrac{1}{3}\arccos\dfrac{1}{2\sqrt{7}}\right)+\sqrt{3}\left(\dfrac{1}{3}\cos\dfrac{1}{2\sqrt{7}}\right)\right)$.

Prove that $\cos\dfrac{\pi}{7}=\dfrac{1}{6}+\dfrac{\sqrt{7}}{6}\left(\cos\left(\dfrac{1}{3}\arccos\dfrac{1}{2\sqrt{7}}\right)+\sqrt{3}\left(\dfrac{1}{3}\cos\dfrac{1}{2\sqrt{7}}\right)\right)$.