Question

How do you plug in answers to find extraneous solutions from a trig equation?

Answer 1

u just plug the solution like you do with regular equations!?
give an example to see it

Answer 2

Uhm ok
Cosx(tanx)=cosx

Answer 3

I got the solutions (degrees)
90, 270, 45, 225

Answer 4

Idk how to put in the solutions though to check?

Answer 5

\(\large\color{slate}{ \cos x(\tan x)=\cos x }\)
\(\large\color{slate}{ \cos x(\tan x)-\cos x=0 }\)
\(\large\color{slate}{ \cos x(\tan x-1)=0 }\)

\(\large\color{slate}{ \cos x=0 }\) or \(\large\color{slate}{ \tan x-1=0 }\)
\(\large\color{slate}{ \tan x=1 }\)

Answer 6

to check a solution just plug it in for x.

Answer 7

9into the original equation)

Answer 8

mhm i know.
But then how are 90 and 270 extraneous?

Answer 9

well for instance 90 wouldn't be and acceptable solution since it makes tan undefined

Answer 10

I think I may be phrasing myself wrong a bit.
Should I put in both cosx=0 and tanx=1 at the same time to check together

Answer 11

any solution that you plug and results in \[\cos x\tan x =\cos x\]

Answer 12

\(\large\color{slate}{ \cos (90)\tan(90)=\cos(90) }\)

\(\large\color{slate}{ \cos (270)\tan(270)=\cos(270) }\)

tan is sin/cos, and so tan(90) and tan(270) is undefined.

Answer 13

i meant \[\cos x\tan x\ne \cos x\]

Answer 14

saying, that any solution that makes cos(x) be zero, is extraneous, because as you plug it into the tangent, your tangent will be undefined.

Answer 15

xapproachesinfinity, it is not an identity, but there are some solutions.

Answer 16

no i'am saying that any solution that makes the equation not true is extra...

Answer 17

Oh I see what you are saying soloman
You see, I used to just put in the fractions or whatever cosx equaled.

Answer 18

correct xapproach

Answer 19

and 90, 270 are examples

Answer 20

yes, basically, for:
\(\large\color{slate}{ \cos (x)\tan(x)=\cos(x) }\)

re-writing: \(\large\color{slate}{ \displaystyle \cos (x)\frac{\sin(x)}{\cos(x)}=\cos(x) }\)

for \(\large\color{slate}{ \cos (x)\tan(x)=\cos(x) }\) you have 2 sets of solutions:

1) where \(\large\color{slate}{ \cos (x)=0 }\)
2) where \(\large\color{slate}{ \tan (x)=1 }\)

Answer 21

But, considering that, \(\large\color{slate}{ \displaystyle \tan(x)=\frac{\sin(x)}{\cos(x)} }\), any solution that makes cos(x) equal to 0 is extraneous, because tan(x) is undefined.

Answer 22

i think i didn't make my point clear lol
thanks solom

Answer 23

oh, i understood:) lol

Answer 24

well, as long the questioner gets it...
karatechopper, do you get what I am saying?

Answer 25

YEAH I DO! THANKS!