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 138999 by bramlexs22 last updated on 21/Apr/21

The number of solutions of equations (√(13−18tan x)) = 6tan x−3 where −2π<x<2π is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions} \\ $$ $$\mathrm{of}\:\mathrm{equations}\:\sqrt{\mathrm{13}−\mathrm{18tan}\:\mathrm{x}}\:=\:\mathrm{6tan}\:\mathrm{x}−\mathrm{3} \\ $$ $$\mathrm{where}\:−\mathrm{2}\pi<\mathrm{x}<\mathrm{2}\pi\:\mathrm{is} \\ $$

Answered by EDWIN88 last updated on 21/Apr/21

(1) 13−18tan x≥0 ; tan x≤((13)/(18)) (2) 13−18tan x=36tan^2 x−36tan x+9 36tan^2 x−18tan x−4=0 18tan^2 x−9tan x−2=0 tan x = ((9 ± 15)/(36)) = { ((tan x=(2/3))),((tan x=−(1/6))) :}

$$\left(\mathrm{1}\right)\:\mathrm{13}−\mathrm{18tan}\:\mathrm{x}\geqslant\mathrm{0}\:;\:\mathrm{tan}\:\mathrm{x}\leqslant\frac{\mathrm{13}}{\mathrm{18}} \\ $$ $$\left(\mathrm{2}\right)\:\mathrm{13}−\mathrm{18tan}\:\mathrm{x}=\mathrm{36tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{36tan}\:\mathrm{x}+\mathrm{9} \\ $$ $$\mathrm{36tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{18tan}\:\mathrm{x}−\mathrm{4}=\mathrm{0} \\ $$ $$\mathrm{18tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{9tan}\:\mathrm{x}−\mathrm{2}=\mathrm{0} \\ $$ $$\mathrm{tan}\:\mathrm{x}\:=\:\frac{\mathrm{9}\:\pm\:\mathrm{15}}{\mathrm{36}}\:=\begin{cases}{\mathrm{tan}\:\mathrm{x}=\frac{\mathrm{2}}{\mathrm{3}}}\\{\mathrm{tan}\:\mathrm{x}=−\frac{\mathrm{1}}{\mathrm{6}}}\end{cases} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com