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