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# C2 factorising a trig equation watch

1. Can someone explain why 2tan2x - tanx = 6 factorises to (2tanx + 3) (tanx-2)

I understand that 3 and 2 were used because they multiply to make 6, but why doesn't (2tanx)(tanx) = 2tan2x2 instead of 2tan2x ?
2. (Original post by jessyjellytot14)
Can someone explain why 2tan2x - tanx = 6 factorises to (2tanx + 3) (tanx-2)

I understand that 3 and 2 were used because they multiply to make 6, but why doesn't (2tanx)(tanx) = 2tan2x2 instead of 2tan2x ?
Simply a mathematical convention. (tan(x))^2 = tan^2 (x).
3. (Original post by jessyjellytot14)
Can someone explain why 2tan2x - tanx = 6 factorises to (2tanx + 3) (tanx-2)

I understand that 3 and 2 were used because they multiply to make 6, but why doesn't (2tanx)(tanx) = 2tan2x2 instead of 2tan2x ?
because

if you still don't understand this, you can always say let tan x = y
then
4. (Original post by jessyjellytot14)
Can someone explain why 2tan2x - tanx = 6 factorises to (2tanx + 3) (tanx-2)

I understand that 3 and 2 were used because they multiply to make 6, but why doesn't (2tanx)(tanx) = 2tan2x2 instead of 2tan2x ?
To make it much easier and clearer, use tanx=y and so you'd have 2y^2 - y - 6 = 0

I love trig so much, I thought I was going to hate it but now I understand it - it's one of my favourite topics!
5. (Original post by jamestg)
To make it much easier and clearer, use tanx=y and so you'd have 2y^2 - y - 6 = 0

I love trig so much, I thought I was going to hate it but now I understand it - it's one of my favourite topics!
Yes, y-substitution might be the better bet here. Simply solve for y, OP, and then solve back for x using x = tan^-1 (y).
6. (Original post by jessyjellytot14)
Can someone explain why 2tan2x - tanx = 6 factorises to (2tanx + 3) (tanx-2)

I understand that 3 and 2 were used because they multiply to make 6, but why doesn't (2tanx)(tanx) = 2tan2x2 instead of 2tan2x ?
I think you've misinterpreted the meaning of tan

tan is a function. Not a term itself.

Let's say you have a function of x called x+1. When you square that, that becomes (x+1)2.

Similarly, tan(x) is a function of x. It means we perform something on the x to get a whole new term. In fact, this means that because it's a single term, you could replace tan(x) with u. That would mean you'd get from (2tanx)(tanx) to (2u)(u) which you know equals 2u2 or 2(tan(x))2. Now as an add on, it's just a convention that we write (tan(x))n as tann(x)
7. Firstly, it must be noted that:
so

In actual fact:

As Student403 mentioned, it is very important to understand that is a function of . Writing alone is completely meaningless as it is not a term in itself but a function which must have an input in order to have an output .

To help you visualise the problem, if you let then your first equation would become . If you factorise this and put back in, you will arrive at the correct answer.

Hope that helps
8. (Original post by jamestg)
To make it much easier and clearer, use tanx=y and so you'd have 2y^2 - y - 6 = 0

I love trig so much, I thought I was going to hate it but now I understand it - it's one of my favourite topics!
(Original post by LelouchViRuge)
because

if you still don't understand this, you can always say let tan x = y
then
Oh okay thank you, that makes so much more sense now!

Say if you had 8sin22x - 2sin2x - 3 = 0 , and you let sinx= y, how would you express y?

Because 8sin2x would then be 8y2 but what about 8sin22x ?
9. (Original post by jessyjellytot14)
Oh okay thank you, that makes so much more sense now!

Say if you had 8sin22x - 2sin2x - 3 = 0 , and you let sinx= y, how would you express y?
4y^2 - y - 3 = 0 I think??? Zacken

I have only had to factorise when the only extra numbers are coefficients
10. (Original post by jessyjellytot14)
Oh okay thank you, that makes so much more sense now!

Say if you had 8sin22x - 2sin2x - 3 = 0 , and you let sinx= y, how would you express y?

Because 8sin2x would then be 8y2 but what about 8sin22x ?
In this case, you'd let to get , where .

This would then get you a quadratic in that you can solve and back-substitute .

In general, if you are given then make the substitution .
11. (Original post by Zacken)
In this case, you'd let to get , where .

This would then get you a quadratic in that you can solve and back-substitute .

In general, if you are given then make the substitution .
Ahhhhhh it makes so much sense, thank you!
12. (Original post by jamestg)
Ahhhhhh it makes so much sense, thank you!

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