A community for students.
Here's the question you clicked on:
 0 viewing
kikij22
 3 years ago
Find all solutions in the interval [0, 2π). 7 tan3x  21 tan x = 0
kikij22
 3 years ago
Find all solutions in the interval [0, 2π). 7 tan3x  21 tan x = 0

This Question is Closed

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.0If you write tan3x as tan(x+2x) you can use the formula for tan(a+b)= (tan a + tan a) / (1 − tan a tan b)

kikij22
 3 years ago
Best ResponseYou've already chosen the best response.0How do you find all of the answers

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.0Hold on, I'm thinking ;)

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.0I first divide the equation by : tan3x  3tanx = 0 Using the sum formula:\[\frac{ \tan x+\tan2x }{ 1\tan x \tan 2x }3\tan x=0\]Now use the formula again, with a=b=x, to get rid of tan2x:\[\frac{ \tan x+\frac{ 2\tan x }{ 1\tan^2x } }{ 1\tan x \frac{ 2\tan x }{ 1\tan^2x } }3\tan x =0\]This is equivalent to\[\frac{ \tan x+\frac{ 2tanx }{ 1\tan^2x } }{ 1\frac{ 2\tan^2x }{ 1\tan^2x } }3\tan x=0\]This is getting a little messy, but we'll keep going on...

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.0Simplify this fractionmess:\[\frac{ \frac{ \tan x(1\tan^2x)+2\tan x }{ 1\tan^2x } }{ \frac{ 1\tan^2x2\tan^2x }{ 1\tan^2x } }3\tan x=0\]Multiply numerator and denomminator by 1tan²x:\[\frac{ 3\tan x\tan^3x }{ 13\tan^2x }=3\tan x\]Multiply LHS and RHS by 13tan²x:\[3\tan x\tan^3x=3\tan x9\tan^3x \Leftrightarrow 8\tan^2x=0\]Now things are looking sunny again! We have tan x = 0. On [0,2pi) there are only the solutions 0 and pi.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.