# Thread: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

1. ## Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

4tan(x) = 6 [ 2tan(x)/1 - tan2(x) ]

Let tan(x) = a

4a (1 - a2) = 12a
1 - a2 = 12a/4a
1 - a2 = 3
therefore, a2 = -2

Which doesn't seem right?
Help would be appreciated, the solutions are 0, pi and 2pi

And how do people type in that math text??!

2. ## Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

Here is a link to the tutorial on how to use LaTex (the math text):

LaTex Tutorial

I will look at your problem now.

3. ## Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

Thanks for the reply and the tutorial. I got the solution, which was really simple. I feel quite silly.

0 = a3 + 2a
0 = a (a2 + 2)
therefore
tan x = 0 or tan2x = -2
x = 0, π or 2π or no solution.

4. ## Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

Can you help me with this one though:

cos(2x)cos($\displaystyle \frac{\pi}{3}$) + sin(2x)sin($\displaystyle \frac{\pi}{3}$) = $\displaystyle \frac{\sqrt{3}}{2}$ for [0, 2$\displaystyle \pi$

\frac{2}{3}

6. ## Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

[math]\frac{1}{2}[\math]

7. ## Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

Okay, ignore all of that

8. ## Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

Originally Posted by iamapineapple
[math]\frac{1}{2}[\math]
Use / to close your brackets, not \.

9. ## Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

$\displaystyle \frac{1}{2}$

y u no work

11. ## Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

$\displaystyle /frac{2}{3}$

12. ## Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

ANYWAY,
cos(2x)cos(π/3) + sin(2x)sin(π/3) = √3/2 for [0, 2π]

so

1/2 cos(2x) + √3/2 sin(2x) = √3/2
cos(2x) + √3 sin(2x) = √3
cos(2x) + 2√3[sin(x)cos(x)] = √3

And then I'm not sure, I tried many ways. Help would be appreciated xox

14. ## Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

Originally Posted by iamapineapple
y u no work
How your mouse over this code:

$\displaystyle \frac{1}{2}$

There may be a problem with [math] tags. Try [tex] instead.

15. ## Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

$\displaystyle \frac{1}{2}$

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