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Category: Algebra

proof-tg-2-36-tg-2-72-5-

Question Number 143384 by mathdanisur last updated on 13/Jun/21 proof:tg2(36°)tg2(72°)=5 Answered by Dwaipayan Shikari last updated on 13/Jun/21 tan36°=sin(36°)cos(36°)=1cos72°sin72°=1514141025=551025$${tan}\mathrm{72}°=\frac{{cos}\mathrm{18}°}{{sin}\mathrm{18}°}=\frac{\sqrt{\mathrm{10}−\mathrm{2}\sqrt{\mathrm{5}}}}{\:\sqrt{\mathrm{5}}−\mathrm{1}}…

Question-143368

Question Number 143368 by mr W last updated on 13/Jun/21 Commented by mr W last updated on 13/Jun/21 Thisisasolvedoldquestion(Q142207).Theansweris$${a}_{{n}} =\frac{\sqrt{\mathrm{2}}\left[\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{2}\left(\mathrm{2}{n}−\mathrm{1}\right)} +\mathrm{1}\right]}{\:\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{2}\left(\mathrm{2}{n}−\mathrm{1}\right)}…