Question Number 207156 by hardmath last updated on 07/May/24
$$\mathrm{Find}:\:\:\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{10}°}\:−\:\frac{\sqrt{\mathrm{3}}}{\mathrm{cos}\:\mathrm{10}°}\:\:=\:\:? \\ $$
Answered by A5T last updated on 07/May/24
$$=\frac{\mathrm{2}{sin}\mathrm{30}}{{sin}\mathrm{10}}−\frac{\mathrm{2}{cos}\mathrm{30}}{{cos}\mathrm{10}}=\frac{\mathrm{2}\left[{sin}\mathrm{30}{cos}\mathrm{10}−{cos}\mathrm{30}{sin}\mathrm{10}\right]}{{sin}\mathrm{10}{cos}\mathrm{10}} \\ $$$$=\frac{\mathrm{2}\left[{sin}\left(\mathrm{30}−\mathrm{10}\right)\right]}{{sin}\mathrm{10}{cos}\mathrm{10}}=\frac{\mathrm{4}{sin}\mathrm{20}}{\mathrm{2}{sin}\mathrm{10}{cos}\mathrm{10}={sin}\mathrm{20}}=\mathrm{4} \\ $$