Question Number 164488 by mathlove last updated on 18/Jan/22
$$\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{30}}−\left(\mathrm{cot}\:\mathrm{30}\right)^{\mathrm{4}} −\left(\mathrm{cot}\:\mathrm{30}\right)^{\mathrm{2}} =…. \\ $$$$\left.{a}\left.\right)\mathrm{sin}\:^{\mathrm{2}} \mathrm{30}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{b}\right)\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{30}} \\ $$$$\left.{c}\left.\right)\mathrm{2sin}\:^{\mathrm{2}} \mathrm{30}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{d}\right)\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{30}} \\ $$
Commented by cortano1 last updated on 18/Jan/22
$$\:=\:\mathrm{2}−\left(\sqrt{\mathrm{3}}\right)^{\mathrm{4}} −\left(\sqrt{\mathrm{3}}\right)^{\mathrm{2}} \\ $$$$\:=\mathrm{2}−\mathrm{9}−\mathrm{3}=−\mathrm{10}\: \\ $$