prove that
![{cos}^{2} \frac{\pi}{8} + {cos}^{2} \frac{3\pi}{8} + {cos}^{2} \frac{5\pi}{8} + { cos }^{2} \frac{7\pi}{8} = 2 {cos}^{2} \frac{\pi}{8} + {cos}^{2} \frac{3\pi}{8} + {cos}^{2} \frac{5\pi}{8} + { cos }^{2} \frac{7\pi}{8} = 2](https://tex.z-dn.net/?f=+%7Bcos%7D%5E%7B2%7D++%5Cfrac%7B%5Cpi%7D%7B8%7D++%2B+%7Bcos%7D%5E%7B2%7D++%5Cfrac%7B3%5Cpi%7D%7B8%7D+%2B++%7Bcos%7D%5E%7B2%7D++%5Cfrac%7B5%5Cpi%7D%7B8%7D++%2B++%7B+cos+%7D%5E%7B2%7D++%5Cfrac%7B7%5Cpi%7D%7B8%7D++%3D+2)
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