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C3 trigonometry question watch

1. Its question 9 of january 2009 C3 for OCR.

9i) By first expanding cos(2X+X) prove that
cos3X = 4cos^3 X - 3cosx

(The x is actually theta in the question)

So I put it into the addition fornular to get cos2x.cosx - sin2x.sinx

Then after this I get stuck. I'm presuming you use the identities such as

(cos2x = 2cos^2x-1)
&
(sin2x = 2sinxcosx)

But it doesn't get me anywhere thanks
2. (Original post by Pistolopete)
Then after this I get stuck. I'm presuming you use the identities such as

(cos2x = 2cos^2x-1)
&
(sin2x = 2sinxcosx)

But it doesn't get me anywhere thanks
Those will do, and you're then only one or two steps away from the solution; have a go.
3. And sin²x+cos²x=1 then you're good to go
4. (Original post by Pistolopete)
x
cos(2x+x)=
cos2xcosx-sin2xsinx=
(2cos^2x-1)cosx-(2sinxcosx)sinx=
2cos^3x-cosx-2sin^2xcosx=
2cos^3x-cosx-2(1-cos^2x)cosx=
2cos^3x-cosx-2cosx+2cos^3x=
4cos^3x-3cosx

Edit: what's with the neg rep?
5. Thankyou for the responses they all helped

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