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Question Number 43543 by peter frank last updated on 11/Sep/18

$$provethat\sqrt{2+\sqrt{2+\sqrt{2+2\cos 8\theta }}}$$$$2\cos \theta$$

Answered by tanmay.chaudhury50@gmail.com last updated on 12/Sep/18

$$\sqrt{2+\sqrt{2+\sqrt{2+2cos8\theta }}}$$$$=\sqrt{2+\sqrt{2+\sqrt{2(1+cos8\theta )}}}$$$$=\sqrt{2+\sqrt{2+\sqrt{4{cos}^{2}4\theta }}}$$$$=\sqrt{2+\sqrt{2+2cos4\theta }}$$$$=\sqrt{2+\sqrt{2(1+cos4\theta )}}$$$$.=\sqrt{2+\sqrt{4{cos}^{2}2\theta }}$$$$=\sqrt{2+2cos2\theta }$$$$=\sqrt{2(1+cos2\theta )}$$$$=\sqrt{4{cos}^2\theta }$$$$=2cos\theta$$$$$$

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