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Question Number 139409 by henderson last updated on 26/Apr/21

$$\mathrm{hi}!$$$$\mathrm{prove}\mathrm{this}:$$$$cos\frac{\pi }{10}+cos\frac{4\pi }{10}+cos\frac{6\pi }{10}+cos\frac{9\pi }{10}=0.$$$$(\mathrm{by}\mathrm{the}\mathrm{easiest}\mathrm{possible}\mathrm{way}...!)$$

Answered by mr W last updated on 26/Apr/21

$$\cos \alpha +\cos (\pi -\alpha )=0$$$$\cos \frac{\pi }{10}+\cos \frac{9\pi }{10}=0$$$$\cos \frac{4\pi }{10}+\cos \frac{6\pi }{10}=0$$$$....=0$$

Commented by henderson last updated on 26/Apr/21

$$\mathrm{waoh}!\mathrm{thank}\mathrm{u}\mathrm{very}\mathrm{much},\mathrm{sir}\mathrm{w}!$$

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