2cos-pi-3-cos-9pi-13-cos-3pi-13-cos-5pi-13-0-

Question Number 20884 by tammi last updated on 06/Sep/17

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

Answered by ajfour last updated on 06/Sep/17

m u s t s t a r t w i t h 2 \cos \frac{π}{13} \dots, T h e n

L . H . S . = \cos (\frac{10 π}{13}) + \cos (\frac{8 π}{13}) +

\cos (\frac{3 π}{13}) + \cos (\frac{5 π}{13})

= \cos (π - \frac{3 π}{13}) + \cos (π - \frac{5 π}{13})

+ \cos (\frac{3 π}{13}) + \cos (\frac{5 π}{13})

= - \cos (\frac{3 π}{13}) - \cos (\frac{5 π}{13}) + \cos (\frac{3 π}{13})

+ \cos (\frac{5 π}{13}) = 0 .

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