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Solve-for-real-numbers-4sin-pi-26-4xsin-3pi-26-4sin-9pi-26-x-13-




Question Number 140193 by mathdanisur last updated on 05/May/21
Solve for real numbers  4sin(π/(26)) + 4xsin((3π)/(26)) + 4sin((9π)/(26)) = x+(√(13))
$${Solve}\:{for}\:{real}\:{numbers} \\ $$$$\mathrm{4}{sin}\frac{\pi}{\mathrm{26}}\:+\:\mathrm{4}{xsin}\frac{\mathrm{3}\pi}{\mathrm{26}}\:+\:\mathrm{4}{sin}\frac{\mathrm{9}\pi}{\mathrm{26}}\:=\:{x}+\sqrt{\mathrm{13}} \\ $$
Answered by Dwaipayan Shikari last updated on 05/May/21
x(1−4sin((3π)/(26)))=4(sin((9π)/(26))+sin(π/(26)))−(√(13))  x=((4(sin((9π)/(26))+sin(π/(16)))−(√(13)))/((1−4sin((3π)/(26)))))
$${x}\left(\mathrm{1}−\mathrm{4}{sin}\frac{\mathrm{3}\pi}{\mathrm{26}}\right)=\mathrm{4}\left({sin}\frac{\mathrm{9}\pi}{\mathrm{26}}+{sin}\frac{\pi}{\mathrm{26}}\right)−\sqrt{\mathrm{13}} \\ $$$${x}=\frac{\mathrm{4}\left({sin}\frac{\mathrm{9}\pi}{\mathrm{26}}+{sin}\frac{\pi}{\mathrm{16}}\right)−\sqrt{\mathrm{13}}}{\left(\mathrm{1}−\mathrm{4}{sin}\frac{\mathrm{3}\pi}{\mathrm{26}}\right)} \\ $$
Commented by mathdanisur last updated on 05/May/21
continued Sir pliz
$${continued}\:{Sir}\:{pliz} \\ $$

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