Will Medal!
If 2tanx/ (1-tan^2x) = 1, then x can equal ____.
Check all that apply.
A) x=5pi/8 + npi
B) x=pi/8 + npi
C) x=3pi/8 + npi
D) x=7pi/8 + npi

- anonymous

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- schrodinger

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- anonymous

I think it is A and B. But this is me taking a guess. I am terrible at trig. Sorry

- welshfella

well first cross multiply to give
2 tanx = 1 - tan^2 x
now rearrange this quadratic:
tan^2 x + 2tanx - 1 = 0
can you factor this?

- anonymous

Yes. I am thinking you factor to get tan^2x = -2tan(x)+1?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- welshfella

no factor as you would any quadratic
like
x^2 + 3x + 2
= (x + 1)(x + 2)

- welshfella

oh sorry - on second look this will not factor
so you need to use the quadratic formula

- anonymous

So would a = tan^2x b =2tanx and c=-1?

- welshfella

no a , b and c are the coefficients of tan^2x and tan x
so a = 1 , b = 2 and c = -1

- anonymous

So x = +/- sqrt (2) in the end right?

- anonymous

*-1 +/- sqrt(2)

- welshfella

-2 +/- sqrt(4 - 4*1*-1) / 2
= -2 +/- sqrt8 / 2
= (-2 +/- 2 * sqrt2 )/ 2
= -1 +/- sqrt2
yep

- anonymous

Awesome! So now do I just plug in this to my original equation?

- welshfella

well they have the answer options in terms of pi
so convert everything to decimals
so for example -1 + sqrt2 = 0.4142
so find the angle in radians which is the tangent of 0.4142
and see if one of the options gives the the same angle

- welshfella

eg angle with tangent 0.4142 = 0.39269 radians
now check if pi/8 gives the same value

- anonymous

Yes it does!

- anonymous

So I'm assuming that is one

- welshfella

ok so thats one result
pi/8 + npi

- welshfella

now try the other value for tan x

- anonymous

-1 - sqrt 2 = -2.4142 degrees right?

- welshfella

yes

- anonymous

Ok so then the radians of -2.4142 is -0.042135

- anonymous

I don't think I did it right

- welshfella

no the -2.4142 is the value of tan x
so you need tan-1(-2.4242)

- anonymous

Oh ok that would make it -1.1781 which is basically the same as 3pi/8 right?

- anonymous

So the answers would be pi/8 + npi and 3pi/8 + npi

- welshfella

yes

- anonymous

Great!! Thank you for taking the time to help me! I feel I really understand now! Thank you!

- anonymous

Weird... I hit the sumit button and it told me it was 5pi/8 instead of 3/pi/8

- welshfella

lets check that out

- myininaya

\[\frac{2tanx}{1-\tan^2x} = 1 \\ \tan(2x)=1\]

- myininaya

\[\tan(u)=1 \text{ when } u=?\]

- welshfella

ahh
i forgot that identity !

- welshfella

u = pi/4 of course
and x will be pi/8

- welshfella

much easier that way lol!

- myininaya

and there is also the u=5pi/4
so yep x=5pi/8

- welshfella

yes

- welshfella

-1.1781 is an incorrect result then?
- an extraneous result right?

- myininaya

does give tan(2x) approx 1
what number are you approximating ?

- myininaya

oh -3pi/8 is what you are approximating

- welshfella

sorry I dont follow you
-yes

- myininaya

that gives 1

- myininaya

when you plug in

- welshfella

and -3pi/8 is equivalent to 5pi/8

- myininaya

is that not included in the solution:
\[\frac{5\pi}{8}+n \pi \\ \text{ if } n=-1 \text{ then } \frac{5\pi}{8}-\pi=\frac{-3\pi}{8}\]
so I'm not sure why you say it is extraneous

- welshfella

no - i was wrong its not extraneous

- welshfella

still i think lehmad learned something along the line...

- anonymous

Yes I learned a lot! Thank you guys for the help.

Looking for something else?

Not the answer you are looking for? Search for more explanations.