Question Number 20702 by tammi last updated on 01/Sep/17
$$\mathrm{tan}\:\mathrm{20}°\mathrm{tan}\:\mathrm{40}°\mathrm{tan}\:\mathrm{80}°=\sqrt{\mathrm{3}} \\ $$
Answered by Tinkutara last updated on 01/Sep/17
$$\mathrm{Using}\:\mathrm{tan}\:\theta\mathrm{tan}\:\left(\mathrm{60}−\theta\right)\mathrm{tan}\:\left(\mathrm{60}+\theta\right)=\mathrm{tan}\:\mathrm{3}\theta \\ $$$$\Rightarrow\mathrm{tan}\:\mathrm{20tan}\:\mathrm{40tan}\:\mathrm{80}=\mathrm{tan}\:\mathrm{60}=\sqrt{\mathrm{3}} \\ $$