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

4tan(x) = 6 [ 2tan(x)/1 - tan^{2}(x) ]

Let tan(x) = a

4a (1 - a^{2}) = 12a

1 - a^{2} = 12a/4a

1 - a^{2} = 3

therefore, a^{2} = -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??!

Thanks in advance

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):

http://mathhelpforum.com/latex-help/...-tutorial.html

I will look at your problem now.

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 = a^{3} + 2a

0 = a (a^{2} + 2)

therefore

tan x = 0 or tan^{2}x = -2

x = 0, π or 2π or no solution.

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$\displaystyle \pi$

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

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

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

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

Quote:

Originally Posted by

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

Use / to close your brackets, not \.

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

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

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

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

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

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

1 Attachment(s)

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

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

Quote:

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.

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

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