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16-cos-2pi-15-cos-4pi-15-cos-8pi-15-cos-14pi-15-




Question Number 79435 by Vishal Sharma last updated on 25/Jan/20
16 cos ((2π)/(15)) cos ((4π)/(15)) cos ((8π)/(15)) cos ((14π)/(15)) =____.
$$\mathrm{16}\:\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{15}}\:\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{15}}\:\mathrm{cos}\:\frac{\mathrm{8}\pi}{\mathrm{15}}\:\mathrm{cos}\:\frac{\mathrm{14}\pi}{\mathrm{15}}\:=\_\_\_\_. \\ $$
Commented by jagoll last updated on 25/Jan/20
Π_(k=1) ^m cos (((kπ)/(2m+1)))=((√2)/2^m )
$$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{m}} {\prod}}\mathrm{cos}\:\left(\frac{\mathrm{k}\pi}{\mathrm{2m}+\mathrm{1}}\right)=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}^{\mathrm{m}} } \\ $$

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