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Question Number 191050 by Shrinava last updated on 16/Apr/23

Prove that:  cos (((2π)/(13))) ∙ cos (((5π)/(13))) ∙ cos (((6π)/(13))) = (((√(13)) − 3)/(16))

$$\mathrm{Prove}\:\mathrm{that}: \\ $$ $$\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{13}}\right)\:\centerdot\:\mathrm{cos}\:\left(\frac{\mathrm{5}\pi}{\mathrm{13}}\right)\:\centerdot\:\mathrm{cos}\:\left(\frac{\mathrm{6}\pi}{\mathrm{13}}\right)\:=\:\frac{\sqrt{\mathrm{13}}\:−\:\mathrm{3}}{\mathrm{16}} \\ $$

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