Question

3tan^3x = tanx

Answer 1

x = 0, -pi/6, pi/6 Rdians

Answer 2

Find all the solutions in the interval (0, 2pi).

Answer 3

Pk, can you explain your answer?

Answer 4

x = 0, -30, 30 Degrees

Answer 5

3tan^3(x) = tan(x)
3tan^2(x) = 1
tan^2(x) = 3
tan (x) = root 3
x= pi/3, 4pi/3

Answer 6

Factor, like myininaya did, then set each part equal to zero and use the unit circle to see where it is equivalent. Then use ASTC to find all solutions.

Answer 7

Ok. Thank you.

Answer 8

my page is going so slow

Answer 9

it should be:
\[3\tan^2(x)-1\]

Answer 10

yep you are right

Answer 11

otherwise, brilliant!

Answer 12

\[3\tan^3x-tanx=tanx(3\tan^2x-1)=0\]

Answer 13

\[tanx=0=> x=2n \pi , x=n \pi , n \in \mathbb{Z}\]
\[\tan^2x=\frac{1}{3}=> tanx=\pm \sqrt{\frac{1}{3}}=\pm \frac{1}{\sqrt{3}}=\pm \frac{\sqrt{3}}{3}\]

Answer 14

So is it fine if I just keep it as my answer but switch what joemath said?

Answer 15

i redid with what joe said

Answer 16

but you need to solve that last equation for x

Answer 17

ok ok, thanks.

Answer 18

i didn't realize you said find solutions in (0,2pi)
so the first equation we just have the answers x=pi

Answer 19

the second equation i would use a calculator