Question

Can someone please factor out for me? I am absolutely stuck. Is it even possible??

4tan^2x - 1 = tan^x

Answer 1

Is it : \(4 \tan ^{2x} - 1 = \tan^x \) or \(4 \tan ^2 x - 1 = \tan ^x \)

Answer 2

I'd reckon its \[4\tan ^{2}x - 1 = \tan x\] since tan needs a variable :S

Answer 3

Yes, that's the correct equation. Do any of you know what the factored form is?

Answer 4

Try replacing tan x with u.
\[4u ^{2} - 1 = u\]
Can you factor this?

Answer 5

no, not using integers anyway

Answer 6

So the final answer would be no solution?

Answer 7

what is the original question?

Answer 8

I believe you can apply the quadratic formula or complete the square, correct me if I'm wrong.

4u^2 - u - 1 = 0
4 (u^2 - 1/4u) - 1 = 0
4(u^2 - 1/4u + 1/64) - 1 - 1/16 = 0
4(u - 1/8)^2 - 17/16 = 0

Then you can substitute tan x = u back in:
4 (tan x - 1/8)^2 - 17/16 = 0
And this should be the solution.

Answer 9

4tan^2 x−1=tanx

Factor into two parenthesis.

I got as far as 4tan^2 x - tanx - 1 = 0

Answer 10

Okay. Thanks! @DoritosHero

Answer 11

No problem :D