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C4 question help needed

6 (a) (i) Given that tan 2x + tan x = 0 , show that tan x = 0
or tan^2x =3 .

^that is the question, it is from the aqa jan 2011 paper.

I have got to 2tanx + tanx(1-tan^2x) / 1 - tan^2x = 0 but i do not know what to do next?

I went on the worked solutions and they have gotten to the same point as me and then have got tanx(2+1-tan^2x) = 0 i do not know how they have got to this??

this is the worked solutions link question 6 (a) (i) : http://www.mrbartonmaths.com/resources/A%20Level%20Past%20Papers/Core%204/2011%20-%20Jan/Core%204%20-%20January%202011%20-%20Written%20Solutions.pdf
Original post by Jack210
6 (a) (i) Given that tan 2x + tan x = 0 , show that tan x = 0
or tan^2x =3 .

^that is the question, it is from the aqa jan 2011 paper.

I have got to 2tanx + tanx(1-tan^2x) / 1 - tan^2x = 0 but i do not know what to do next?

I went on the worked solutions and they have gotten to the same point as me and then have got tanx(2+1-tan^2x) = 0 i do not know how they have got to this??

this is the worked solutions link question 6 (a) (i) : http://www.mrbartonmaths.com/resources/A%20Level%20Past%20Papers/Core%204/2011%20-%20Jan/Core%204%20-%20January%202011%20-%20Written%20Solutions.pdf


Just multiply through by 1−tan⁡2x1-\tan^2 x then factor out tan⁡x\tan x
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Jack210
OP
12
Original post by RDKGames
Just multiply through by 1−tan⁡2x1-\tan^2 x then factor out tan⁡x\tan x


i've tried doing that, i think i'm going wrong somewhere :/ could you show me step by step how you do it please?
Original post by Jack210
i've tried doing that, i think i'm going wrong somewhere :/ could you show me step by step how you do it please?


Not much room to go wrong tbh...


2tan⁡x+tan⁡x(1−tan⁡2x)1−tan⁡2x=0\dfrac{2\tan x + \tan x(1-\tan^2 x) }{1- \tan^2 x } = 0

⇒2tan⁡x+tan⁡x(1−tan⁡2x)=0\Rightarrow 2\tan x + \tan x (1-\tan^2 x ) = 0

⇒tan⁡x(2+1−tan⁡2x)=0\Rightarrow \tan x(2+1-\tan^2 x ) = 0
Original post by Jack210
6 (a) (i) Given that tan 2x + tan x = 0 , show that tan x = 0
or tan^2x =3 .

^that is the question, it is from the aqa jan 2011 paper.

I have got to 2tanx + tanx(1-tan^2x) / 1 - tan^2x = 0 but i do not know what to do next?

I went on the worked solutions and they have gotten to the same point as me and then have got tanx(2+1-tan^2x) = 0 i do not know how they have got to this??

this is the worked solutions link question 6 (a) (i) : http://www.mrbartonmaths.com/resources/A%20Level%20Past%20Papers/Core%204/2011%20-%20Jan/Core%204%20-%20January%202011%20-%20Written%20Solutions.pdf

Listen baby thats so easy.
Use the double angle formula to turn tan2x into the double angle identity. then times by the denominator what ever it is then FACTORISE
Original post by RDKGames
Not much room to go wrong tbh...


2tan⁡x+tan⁡x(1−tan⁡2x)1−tan⁡2x=0\dfrac{2\tan x + \tan x(1-\tan^2 x) }{1- \tan^2 x } = 0

⇒2tan⁡x+tan⁡x(1−tan⁡2x)=0\Rightarrow 2\tan x + \tan x (1-\tan^2 x ) = 0

⇒tan⁡x(2+1−tan⁡2x)=0\Rightarrow \tan x(2+1-\tan^2 x ) = 0


Yes G that is correct, I did my C4 mock its favjing basic innit?
Reply 6
Avatar for Jack210
Jack210
OP
12
Original post by RDKGames
Not much room to go wrong tbh...


2tan⁡x+tan⁡x(1−tan⁡2x)1−tan⁡2x=0\dfrac{2\tan x + \tan x(1-\tan^2 x) }{1- \tan^2 x } = 0

⇒2tan⁡x+tan⁡x(1−tan⁡2x)=0\Rightarrow 2\tan x + \tan x (1-\tan^2 x ) = 0

⇒tan⁡x(2+1−tan⁡2x)=0\Rightarrow \tan x(2+1-\tan^2 x ) = 0


i am so confused because i don't understand where the denominator has gone? if you multiply by 1-tan^2x wouldn't the numerators numbers be multiplied by it? and also i don't get how 2tanx+tanx(1-tan^2x) has got to tanx(2+1-tan^2x)
(edited 6 years ago)
Original post by Jack210
i am so confused because i don't understand where the denominator has gone? if you multiply by 1-tan^2x wouldn't the numerators numbers be multiplied by it? and also i don't get how 2tanx+tanx(1-tan^2x) has got to tanx92+1-tan^2x)


The 1−tan⁡2x1-\tan^2 x is the denominator, multiplying both sides of the equation by it cancels it out.
Then just factor out tan⁡x\tan x, mate.

These shouldn't be issues at C4.
Original post by Jack210
i am so confused because i don't understand where the denominator has gone? if you multiply by 1-tan^2x wouldn't the numerators numbers be multiplied by it? and also i don't get how 2tanx+tanx(1-tan^2x) has got to tanx(2+1-tan^2x)


You're multiplying the left hand side and the right hand side by the same thing, not the numerator and the denominator.

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