1. Nov 15, 2013

### Kishlay

1. The problem statement, all variables and given/known data

tanx+tan2x+root3tanxtan2x=root3
find x........

2. Relevant equations

3. The attempt at a solution
i have tried a lot and always ended with a complicated cubic equation...........

2. Nov 15, 2013

### Staff: Mentor

I'd try using the tan(a+b) identity to reduce the equation into terms with tan(x) factors.

what is the root3 you mention? Is it some arbitrary constant?

3. Nov 15, 2013

### Kishlay

yes I have tried the same thing as you have said
root3 is same as √3

4. Nov 15, 2013

Do you mean:
$tan(x)+tan(2x)+\sqrt{3}*tan(x)*tan(2x)=\sqrt{3}$ ?

5. Nov 15, 2013

### Staff: Mentor

and you tried using the identity tan(2x) = 2tan(x) / (1-tan^2(x))

and then collecting terms to create a cubic equation in tan(x) thats equal to zero.

6. Nov 15, 2013

### Kishlay

so??

7. Nov 15, 2013

### Kishlay

yes..
how did you typed it??

8. Nov 15, 2013

### Staff: Mentor

It is not enough to say what you have tried. You need to show us what you have tried.

9. Nov 15, 2013

### Kishlay

yes.... how did you typed it???

10. Nov 15, 2013

### Kishlay

i have used the identity of tan(A+B)
then i simplified it and got a cubic equation in tanx
and i dont know how to solve a cubic.........
i am a high school student :)

11. Nov 15, 2013

### Staff: Mentor

The PF website provides an advanced editor where you can enter mathematical expressions with subscripts, superscripts, summations, integrals...

Use the "Go Advanced" button to the right of the "Post Quick Reply" button next time.

12. Nov 15, 2013

Latex-Quote it and see how I've written it.You have to write
Code (Text):
$and$
around the sentence.

13. Nov 15, 2013

### Kishlay

ok...:)

14. Nov 15, 2013

### Staff: Mentor

So show us the cubic equation.

The goal of the PF forum is help you with your homework not do it for you.

15. Nov 15, 2013

### ehild

No need to solve a cubic equation.
Notice that √3=tan(π/3)

You can rearrange the equation as

$$\tan(2x)(1+\sqrt3 \tan(x))=\sqrt3 - \tan(x)$$

that is

$$\tan(2x)=\frac{\sqrt3 - \tan(x)}{1+\sqrt3 \tan(x)}$$

Recall that

$$\tan(a-b)=\frac{\tan(a) - \tan(b)}{1+\tan(a) \tan(b)}$$

ehild

16. Nov 15, 2013

### Kishlay

i have got this equation
(tanx)3-3$\sqrt{}3$(tanx)2-3tanx+$\sqrt{}3$ =0

17. Nov 15, 2013

### Kishlay

thanks.......!!

18. Nov 15, 2013

### ehild

You are welcome

ehild

19. Nov 15, 2013

### Staff: Mentor

dont forget to thank ehild via the thanks button.

20. Nov 15, 2013

### ehild

It had been done and very properly

ehild