Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 14330 by myintkhaing last updated on 01/Jun/17

tanθ+tan2θ=tan3θ  ((tanθ+tan2θ)/(1−tanθtan2θ))(1−tanθtan2θ)=tan3θ  tan3θ(1−tanθtan2θ)=tan3θ  tanθtan2θtan3θ 0  3θ=kπ, where k=0,1,2,3,...  θ=((kπ)/3)  tanθ=0  or  tan2θ=0 or tan 3θ = 0  θ=mπ, where m=0,1,2,3,...  2θ=nπ, where n=0,1,2,3,...  θ=((nπ)/2) but θ∉(((p+1)π)/2), p=0,1,2,3,...  The exhaustive set ={θ/θ=((kπ)/3) or θ=mπ}

$${tan}\theta+{tan}\mathrm{2}\theta={tan}\mathrm{3}\theta \\ $$$$\frac{{tan}\theta+{tan}\mathrm{2}\theta}{\mathrm{1}−{tan}\theta{tan}\mathrm{2}\theta}\left(\mathrm{1}−{tan}\theta{tan}\mathrm{2}\theta\right)={tan}\mathrm{3}\theta \\ $$$${tan}\mathrm{3}\theta\left(\mathrm{1}−{tan}\theta{tan}\mathrm{2}\theta\right)={tan}\mathrm{3}\theta \\ $$$${tan}\theta{tan}\mathrm{2}\theta{tan}\mathrm{3}\theta\:\mathrm{0} \\ $$$$\mathrm{3}\theta={k}\pi,\:{where}\:{k}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},... \\ $$$$\theta=\frac{{k}\pi}{\mathrm{3}} \\ $$$${tan}\theta=\mathrm{0}\:\:{or}\:\:{tan}\mathrm{2}\theta=\mathrm{0}\:{or}\:{tan}\:\mathrm{3}\theta\:=\:\mathrm{0} \\ $$$$\theta={m}\pi,\:{where}\:{m}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},... \\ $$$$\mathrm{2}\theta={n}\pi,\:{where}\:{n}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},... \\ $$$$\theta=\frac{{n}\pi}{\mathrm{2}}\:{but}\:\theta\notin\frac{\left({p}+\mathrm{1}\right)\pi}{\mathrm{2}},\:{p}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},... \\ $$$${The}\:{exhaustive}\:{set}\:=\left\{\theta/\theta=\frac{{k}\pi}{\mathrm{3}}\:{or}\:\theta={m}\pi\right\} \\ $$

Commented by Tinkutara last updated on 30/May/17

Thanks!

$$\mathrm{Thanks}! \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com