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# C3 trigonometry hard ques. watch

1. By writing the following equations as quadratics in tan θ/2,solve,in the
interval 0 ≤ θ ≤ 360°:

(i) sinθ + 2cosθ = 1

So i was thinking of using this formula:
tan2θ= 2tanθ/1-2tan^2θ
which can be rewritten into:
tanθ=2tanθ/2/1-tan^2θ/2

Tanθ/2= t

so 2t/1-t^2

But when i checked the working out, it wanted:

2t/1+t^2

Thanks
2. (Original post by Lilly1234567890)
By writing the following equations as quadratics in tan θ/2,solve,in the
interval 0 ≤ θ ≤ 360°:

(i) sinθ + 2cosθ = 1

So i was thinking of using this formula:
tan2θ= 2tanθ/1-2tan^2θ
which can be rewritten into:
tanθ=2tanθ/2/1-tan^2θ/2

Tanθ/2= t

so 2t/1-t^2

But when i checked the working out, it wanted:

2t/1+t^2

Thanks
what board are you doing please?
3. (Original post by TeeEm)
what board are you doing please?
Edexcel
4. (Original post by Lilly1234567890)
Edexcel
this will never come up in an edexcel maths or further maths paper.
it comes from older/other boards and you require to use the "LITTLE t" identities

I will post a few examples in a few minutes for you to see how these work
5. (Original post by TeeEm)
this will never come up in an edexcel maths or further maths paper.
it comes from older/other boards and you require to use the "LITTLE t" identities

I will post a few examples in a few minutes for you to see how these work
Thanks!
the question is on pg.119 Q7
so i thought it was part of the syllabus
6. (Original post by Lilly1234567890)
Thanks!
the question is on pg.119 Q7
so i thought it was part of the syllabus
these results are for enrichment material these days

here are 3 questions

the identities you have to prove in part (a) are common knowledge to mathematicians
Attached Images
7. PDF.pdf (426.9 KB, 70 views)
8. (Original post by Lilly1234567890)
By writing the following equations as quadratics in tan θ/2,solve,in the
interval 0 ≤ θ ≤ 360°:

(i) sinθ + 2cosθ = 1

So i was thinking of using this formula:
tan2θ= 2tanθ/1-2tan^2θ
which can be rewritten into:
tanθ=2tanθ/2/1-tan^2θ/2

Tanθ/2= t

so 2t/1-t^2

But when i checked the working out, it wanted:

2t/1+t^2

Thanks
You have shown that which is correct.

The next step is to figure out what is.

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