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

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• May 21st 2013, 02:27 AM
iamapineapple
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??!
• May 21st 2013, 02:57 AM
Qwob
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.
• May 21st 2013, 03:26 AM
iamapineapple
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.
• May 21st 2013, 03:38 AM
iamapineapple
Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?
Can you help me with this one though:

cos(2x)cos([LaTeX ERROR: Compile failed] ) + sin(2x)sin([LaTeX ERROR: Compile failed] ) = [LaTeX ERROR: Compile failed] for [0, 2[LaTeX ERROR: Compile failed]
• May 21st 2013, 03:40 AM
iamapineapple
Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?
\frac{2}{3}
• May 21st 2013, 03:40 AM
iamapineapple
Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?
[tex]\frac{1}{2}[\math]
• May 21st 2013, 03:42 AM
iamapineapple
Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?
Okay, ignore all of that
• May 21st 2013, 03:42 AM
Paze
Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?
Quote:

Originally Posted by iamapineapple
[tex]\frac{1}{2}[\math]

Use / to close your brackets, not \.
• May 21st 2013, 03:44 AM
iamapineapple
Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?
[LaTeX ERROR: Compile failed]
• May 21st 2013, 03:45 AM
iamapineapple
Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?
y u no work :(
• May 21st 2013, 03:45 AM
iamapineapple
Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?
[LaTeX ERROR: Compile failed]
• May 21st 2013, 03:50 AM
iamapineapple
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
• May 21st 2013, 05:16 AM
ibdutt
Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?
• May 21st 2013, 09:16 AM
Paze
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:

$\frac{1}{2}$

There may be a problem with [tex] tags. Try [tex] instead.
• May 22nd 2013, 04:53 AM
iamapineapple
Re: Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?
$\frac{1}{2}$
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