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Question Number 29833 by abdo imad last updated on 12/Feb/18

$$find{cos}^4\left(\frac{\pi }{8}\right)+{cos}^4\left(\frac{3\pi }{8}\right)+{cos}^4\left(\frac{5\pi }{8}\right)+{cos}^4\left(\frac{7\pi }{8}\right).$$

Answered by MJS last updated on 14/Feb/18

$$\cos \left(\frac{\pi }{8}\right)=-\cos \left(\frac{7\pi }{8}\right)=\frac{\sqrt{2+\sqrt{2}}}{2}$$$$\cos \left(\frac{3\pi }{8}\right)=-\cos \left(\frac{5\pi }{8}\right)=\frac{\sqrt{2-\sqrt{2}}}{2}$$$$\mathrm{so}\mathrm{the}\mathrm{answer}\mathrm{is}\frac{3}{2}$$

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