Question

Solve the following equation for 0 degrees < x < 360 degrees

3 tan x + cot x = 3 sec x

I will post my attempt at an answer.

Answer 1

\[3tanx+\frac{1}{tanx}=3\sqrt{1+tan^{2}}\]
multiply both sides by itself
\[3tan^{2}x+6+\frac{1}{tan^{2}x}=9+9tan^{2}\]

Answer 2

that should be
\[9tan^{2}x+6+\frac{1}{tan^{2}x}=9+9tan^{2}\]

Answer 3

\[6+\frac{1}{tan^{2}x}=9\]
\[\frac{1}{tan^{2}x}=3\]
\[tan^{2}x=\frac{1}{3}\]
\[tanx=\frac{1}{+-\sqrt3}\]

Answer 4

x = 30, 210, 150, 330

The answer my textbook gives is
30, 90, 150

Help?

Answer 5

"multiply both sides by itself"

Answer 6

thats where you went wrong I beleive

Answer 7

You did not correctly square the left side

Answer 8

Sorry but did you check the very next post.

Answer 9

nope stopped when i hit the mistake =P

Answer 10

I shall continue

Answer 11

@amistre64 ?

Answer 12

i tend to put everything into sins and coss

Answer 13

Maybe I'll get the book's answer if I try that. It is still frustrating if I don't know what is wrong with what happened here though.

I can definitely see a way to solve this with sins and coss now that you mention it.

Answer 14

\[3\frac{s}{c}+\frac{c}{s}=3\frac{1}{c}\]
\[3s+\frac{cc}{s}=3\]
\[3s+\frac{1-ss}{s}=3\]
\[\frac{3ss+(1-ss)}{s}=\frac{3s}{s}\]
\[2s^2+1=3s\]
\[2s^2-3s+1=0\]

might be one option to try

Answer 15

I just solved it using your suggestion and it matches. Thanks.

Would be nice to know the problem with my initial attempt though.

Answer 16

Possible domain issue??

Answer 17

3t*3t not= 3t^2 is one error (possibly typo?)

Answer 18

you corrected with 2nd post

Answer 19

if i were to take a guess, i would say that squaring should be a last resort since it has a tendency to introduce extraneous solutions at times

Answer 20

Well thanks for the help.

Answer 21

good luck ;)