Question

What is ( (tan^2)x)(2x)=3

Answer 1

\[2x \tan^{2}(x) = 3\]

is that it?

Answer 2

Might be. I'm looking at it like O______________________o

Answer 3

I think you have to use \(\cos ^2x = 1-\sin^2 x\)

Answer 4

But even then I'm not completely sure of the trick here.

Answer 5

Are we trying to solve for x in this problem?

Answer 6

It's a non-linear problem, and is not likely to have an elementary solution.
Try numerical methods.

Answer 7

@Asiah321 could you confirm the equation?

what @DanJS posted can not be solved algebraically

Answer 8

\[(\tan ^{2}x) \space (2x) \space = 3\]

Answer 9

\[(tanx)^{2} \space (2x) \space =3\]

Answer 10

You can't actually solve this by hand because you can't get x alone
tan^2 x means (tanx)^2 If you want to get x, you need a calculator
You would either have to graph y = (tanx)^2*2x and y = 3 and
find where they intersect Or graph y = (tanx)^2*2x - 3 and find where it hits the x-axis

Answer 11

There are 4 roots between 0 & 2pi.
The first one is around 0.9093 rad.

Answer 12

Newton's method would come handy for this, or even bisection method.

Answer 13

Right

Answer 14

I agree with that too. Whichever methods allow you to approximate roots

Answer 15

Newton's method might be a drag though since you would need to do it for each root

Answer 16

i just guessed that was his question, i could be wrong

Answer 17

Just using a calculator straight out seems to be the easiest method here
You would need a calculator for newton's method in any case

Answer 18

For those interested, I graphed it as suggeste by @Miracrown, it gives roots at 0.9,2.5,3.7,and 5.8 between 0 and 2pi, for those who would give it a try.

Answer 19

Yes, I agree ^

Answer 20

and for the Newton fans, y'(x)=2tan^2(x)+4x tan(x)/cos(x)^2

Answer 21

@DanJS we're all in the dark, and you're the only one with a candle. :)
It's up to @Asiah321 to correct your best interpretation if it's not correct.