# Thread: Really Hard Trig Equation

1. ## Really Hard Trig Equation

tan^3x-9tan^2x-3tanx+3=0

Solve for x. Thanks for helping.

2. Originally Posted by GamesonPlanes
tan^3x-9tan^2x-3tanx+3=0

Solve for x. Thanks for helping.
Are you sure that is the correct equation?

3. Yes, that is the right one. Its a very hard problem, but its the right one.

4. Originally Posted by GamesonPlanes
Yes, that is the right one. Its a very hard problem, but its the right one.
Really? solve tan(u)^3-9tan(u)^2+3tan(u)+3=0 - Wolfram|Alpha

5. Im ABSOLUTELY sure its the right question. And its minus 3tanx btw.

6. Originally Posted by GamesonPlanes
Im ABSOLUTELY sure its the right question.
My point was that it looks like it has imaginary solutions. There may be some trig identity, look for one. Otherwise, let $\displaystyle u=\tan(x)$ attempt to solve $\displaystyle u^3-9u^2-3u+3=0$ and go from there.

7. Originally Posted by Drexel28
My point was that it looks like it has imaginary solutions. There may be some trig identity, look for one. Otherwise, let $\displaystyle u=\tan(x)$ attempt to solve $\displaystyle u^3-9u^2-3u+3=0$ and go from there.
factorise x^3 - 9x^2 - 3x + 3 - Wolfram|Alpha

And since Wolfram finds it difficult ....