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 14268 by Tinkutara last updated on 30/May/17

If tanθ + tan2θ = tan3θ, find the  exhaustive set of values of θ satisfying  the given equation.

$$\mathrm{If}\:\mathrm{tan}\theta\:+\:\mathrm{tan2}\theta\:=\:\mathrm{tan3}\theta,\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{exhaustive}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\theta\:\mathrm{satisfying} \\ $$$$\mathrm{the}\:\mathrm{given}\:\mathrm{equation}. \\ $$

Answered by linkelly0615 last updated on 30/May/17

∵tan3θ=((tanθ+tan2θ)/(1−tanθtan2θ))=tanθ+tan2θ  ∴1−tanθtan2θ=1  ∴tanθtan2θ=0 ,and θ∉(n+1/2)π , n∈Z  ∴θ=kπ , k∈Z#

$$\because{tan}\mathrm{3}\theta=\frac{{tan}\theta+{tan}\mathrm{2}\theta}{\mathrm{1}−{tan}\theta{tan}\mathrm{2}\theta}={tan}\theta+{tan}\mathrm{2}\theta \\ $$$$\therefore\mathrm{1}−{tan}\theta{tan}\mathrm{2}\theta=\mathrm{1} \\ $$$$\therefore{tan}\theta{tan}\mathrm{2}\theta=\mathrm{0}\:,{and}\:\theta\notin\left({n}+\mathrm{1}/\mathrm{2}\right)\pi\:,\:{n}\in\mathbb{Z} \\ $$$$\therefore\theta={k}\pi\:,\:{k}\in\mathbb{Z}# \\ $$

Commented by Tinkutara last updated on 30/May/17

What will be the complete set of  solution?

$$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{complete}\:\mathrm{set}\:\mathrm{of} \\ $$$$\mathrm{solution}? \\ $$

Commented by prakash jain last updated on 30/May/17

another possibility is  tan θ+tan 2θ=0

$${another}\:{possibility}\:{is} \\ $$$$\mathrm{tan}\:\theta+\mathrm{tan}\:\mathrm{2}\theta=\mathrm{0} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com