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Question Number 75040 by mathocean1 last updated on 06/Dec/19
Please can you help me to   to show that:  cos ((47Π)/(13))=sin ((23Π)/(26))=sin((3Π)/(26))
$$\mathrm{Please}\:\mathrm{can}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\: \\ $$$$\mathrm{to}\:\mathrm{show}\:\mathrm{that}: \\ $$$$\mathrm{cos}\:\frac{\mathrm{47}\Pi}{\mathrm{13}}=\mathrm{sin}\:\frac{\mathrm{23}\Pi}{\mathrm{26}}=\mathrm{sin}\frac{\mathrm{3}\Pi}{\mathrm{26}} \\ $$
Answered by Kunal12588 last updated on 06/Dec/19
cos((47π)/(13))=cos(((52π−5π)/(13)))=cos(4π−((5π)/(13)))  =cos(((5π)/(13)))=sin((π/2)+((5π)/(13)))=sin((23π)/(26))  =sin((26π−3π)/(26))=sin(π−((3π)/(26)))=sin((3π)/(26))
$${cos}\frac{\mathrm{47}\pi}{\mathrm{13}}={cos}\left(\frac{\mathrm{52}\pi−\mathrm{5}\pi}{\mathrm{13}}\right)={cos}\left(\mathrm{4}\pi−\frac{\mathrm{5}\pi}{\mathrm{13}}\right) \\ $$$$={cos}\left(\frac{\mathrm{5}\pi}{\mathrm{13}}\right)={sin}\left(\frac{\pi}{\mathrm{2}}+\frac{\mathrm{5}\pi}{\mathrm{13}}\right)={sin}\frac{\mathrm{23}\pi}{\mathrm{26}} \\ $$$$={sin}\frac{\mathrm{26}\pi−\mathrm{3}\pi}{\mathrm{26}}={sin}\left(\pi−\frac{\mathrm{3}\pi}{\mathrm{26}}\right)={sin}\frac{\mathrm{3}\pi}{\mathrm{26}} \\ $$
Commented by mathocean1 last updated on 07/Dec/19
thank you sir
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$

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