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Question Number 21259 by oyshi last updated on 17/Sep/17

$$2\cos \frac{\pi }{13}\cos \frac{9\pi }{13}+\cos \frac{3\pi }{13}+\cos \frac{5\pi }{13}=0$$

Answered by myintkhaing last updated on 18/Sep/17

$$\mathrm{L}.\mathrm{H}.\mathrm{S}=\cos \frac{10\pi }{13}+\cos \frac{8\pi }{13}+\cos \frac{3\pi }{13}+\cos \frac{5\pi }{13}$$$$=\cos (\pi -\frac{3\pi }{13})+\cos (\pi -\frac{5\pi }{13})+\cos \frac{3\pi }{13}+\cos \frac{5\pi }{13}$$$$=-\cos \frac{3\pi }{13}-\cos \frac{5\pi }{13}+\cos \frac{3\pi }{13}+\cos \frac{5\pi }{13}=0$$

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