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tan-20-tan-40-tan-80-3-




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

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