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Question Number 208130 by efronzo1 last updated on 06/Jun/24

$$\frac{1}{\cos \mathrm{x}-\cos 3\mathrm{x}}+\frac{1}{\cos \mathrm{x}-\cos 5\mathrm{x}}+$$$$\frac{1}{\cos \mathrm{x}-\cos 7\mathrm{x}}+\frac{1}{\cos \mathrm{x}-\cos 11\mathrm{x}}=?$$

Answered by Ghisom last updated on 06/Jun/24

$$\mathrm{let}{c}_n=\cos nx$$$$=-\frac{2c_{10}+4c_8+8c_6+10c_4+16c_2+7}{c_{13}+c_9-c_3-c_1}$$$$\mathrm{not}\mathrm{sure}\mathrm{why}\mathrm{I}\mathrm{did}\mathrm{this},\mathrm{maybe}\mathrm{I}\mathrm{thought}$$$$\mathrm{it}\mathrm{would}\mathrm{be}\mathrm{something}\mathrm{interesting}...$$

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