Author Topic: 4tan(x) = 6tan(2x)? Solve for x? (Read 758 times) Tweet Share

ahat · « **on:** May 21, 2013, 07:25:28 pm »

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

b^3 · « **Reply #1 on:** May 21, 2013, 08:00:49 pm »

When you divided by $a$ you lose solutions, since you're dividing by $\tan(x)$ . What you need to do is move everything to the one side, and factorise the cubic, and then you'll get one factor that doesn't solve anything (the one you've already got) and another factor which gives the solutions that you have there.

Spoiler

$\begin{alignedat}{1}4\tan\left(x\right) & =\frac{12\tan\left(x\right)}{1-\tan^{2}\left(x\right)} \\ 4\tan\left(x\right)-4\tan^{3}\left(x\right) & =12\tan\left(x\right) \\ 4\tan^{3}\left(x\right)+8\tan\left(x\right) & =0 \\ \tan\left(x\right)\left(\tan^{2}\left(x\right)+2\right) & =0 \\ \tan\left(x\right)=0 & \:\:\text{or}\:\:\tan^{2}\left(x\right)+2=0 \\ x=0,\:\pi,\:2\pi \end{alignedat} $

ahat · « **Reply #2 on:** May 21, 2013, 08:23:03 pm »

Oh my, so simple. I feel so silly now. Thankyou.

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

Why did I spend so long on this!! D:
But thanks! You instigated this solution!

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Author Topic: 4tan(x) = 6tan(2x)? Solve for x? (Read 758 times) Tweet Share

ahat

4tan(x) = 6tan(2x)? Solve for x?

b^3

Re: 4tan(x) = 6tan(2x)? Solve for x?

ahat

Re: 4tan(x) = 6tan(2x)? Solve for x?

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