Question Number 181066 by Shrinava last updated on 21/Nov/22
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression}: \\ $$$$\mathrm{2arcctg}\left(\mathrm{tg3}\right)\:−\:\mathrm{3arctg}\left(\mathrm{ctg2}\right) \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{2}\left.\pi\left.−\mathrm{3}\:\:\mathrm{b}\right)\mathrm{12}\:\:\mathrm{c}\right)−\mathrm{6}\:\:\mathrm{d}\right)\pi−\mathrm{4}/\mathrm{2}\:\:\mathrm{e}\right)\mathrm{3}\pi/\mathrm{2} \\ $$
Commented by mr W last updated on 22/Nov/22
$${all}\:{answers}\:{given}\:{are}\:{wrong}! \\ $$
Answered by mr W last updated on 22/Nov/22
$$\mathrm{2}\:\mathrm{cot}^{−\mathrm{1}} \left(\mathrm{tan}\:\mathrm{3}\right)=\mathrm{2}\left(\frac{\pi}{\mathrm{2}}−\mathrm{3}\right)=\pi−\mathrm{6} \\ $$$$\mathrm{3}\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{cot}\:\mathrm{2}\right)=\mathrm{3}\left(\frac{\pi}{\mathrm{2}}−\mathrm{2}\right)=\frac{\mathrm{3}\pi}{\mathrm{2}}−\mathrm{6} \\ $$$$….=\pi−\mathrm{6}−\left(\frac{\mathrm{3}\pi}{\mathrm{2}}−\mathrm{6}\right)=−\frac{\pi}{\mathrm{2}}\:\checkmark \\ $$
Commented by Shrinava last updated on 24/Nov/22
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{dera}\:\mathrm{professor} \\ $$