Y by Adventure10, Mango247
Prove that:
![$\frac{1}{\sqrt[3]{\cos \frac{\pi}{7}}} - \frac{1}{\sqrt[3]{\cos \frac{2\pi}{7}}} +\frac{1}{\sqrt[3]{\cos \frac{3\pi}{7}}} =\sqrt[3]{6\sqrt[3]{7}-8}$](//latex.artofproblemsolving.com/6/c/6/6c681499e8994dc76f94fbcb28cb6a1b7dcdc861.png)
![$\frac{1}{\sqrt[3]{\cos \frac{\pi}{9}}} - \frac{1}{\sqrt[3]{\cos \frac{2\pi}{9}}} +\frac{1}{\sqrt[3]{\cos \frac{5\pi}{9}}} =\sqrt[3]{6-6\sqrt[3]{9}}$](//latex.artofproblemsolving.com/e/9/7/e97f301b757ba2040b6607cfca47e66f6f8fde5c.png)
![$\frac{1}{\sqrt[3]{\cos \frac{\pi}{7}}} - \frac{1}{\sqrt[3]{\cos \frac{2\pi}{7}}} +\frac{1}{\sqrt[3]{\cos \frac{3\pi}{7}}} =\sqrt[3]{6\sqrt[3]{7}-8}$](http://latex.artofproblemsolving.com/6/c/6/6c681499e8994dc76f94fbcb28cb6a1b7dcdc861.png)
![$\frac{1}{\sqrt[3]{\cos \frac{\pi}{9}}} - \frac{1}{\sqrt[3]{\cos \frac{2\pi}{9}}} +\frac{1}{\sqrt[3]{\cos \frac{5\pi}{9}}} =\sqrt[3]{6-6\sqrt[3]{9}}$](http://latex.artofproblemsolving.com/e/9/7/e97f301b757ba2040b6607cfca47e66f6f8fde5c.png)
This post has been edited 1 time. Last edited by _Mark_01, May 20, 2014, 7:46 PM
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