Question Number 53340 by aseerimad last updated on 20/Jan/19
Answered by tanmay.chaudhury50@gmail.com last updated on 20/Jan/19
$${a}=\mathrm{18}^{{o}} \\ $$$$ \\ $$$${method}\:\mathrm{1} \\ $$$$\frac{{sin}\mathrm{54}}{{cos}\mathrm{54}}−\frac{{sin}\mathrm{36}}{{cos}\mathrm{36}} \\ $$$$\frac{{sin}\mathrm{54}{cos}\mathrm{36}−{cos}\mathrm{54}{sin}\mathrm{36}}{{cos}\mathrm{54}{cos}\mathrm{36}} \\ $$$$\frac{{sin}\left(\mathrm{54}−\mathrm{36}\right)}{{cos}\mathrm{54}{cos}\mathrm{36}} \\ $$$$=\frac{\mathrm{2}{sin}\mathrm{18}}{\mathrm{2}{cos}\mathrm{54}{cos}\mathrm{36}} \\ $$$$=\frac{\mathrm{2}{sin}\mathrm{18}}{{cos}\mathrm{90}+{cos}\mathrm{18}} \\ $$$$=\mathrm{2}{tan}\mathrm{18} \\ $$$${method}\:\mathrm{2} \\ $$$${put}\:{the}\:{value}\:{of}\:{sin}\mathrm{18}\:,{cos}\mathrm{18}\:{and}\:{sin}\mathrm{36}\:{and} \\ $$$${cos}\:\mathrm{36}\:{etc}... \\ $$