Thread: Where am I messing up? (Proof) [cos3x = 4cos^3x-3cosx]

Hi, I am doing a proof and I have it all down but in the last step it seems as though I distributed my negatives incorrectly. However, I cannot seem to find where. Any help would be great! Thanks!

cos3x = 4cos^3x-3cosx is the proof. So I did:

cos3x =
cos (2x + x) =
cos2xcosx+sin2xsinx =
cosx (2cos^2x-1) + sinx(2sinxcosx) =
2cos^3x - cosx + 2sin^2xcosx =
2cos^3x - cosx + 2(1-cos^2x)cosx =
2cos^3x - cosx + 2cosx - 2cos^3x

However, 2cos^3x - cosx + 2cosx - 2cos^3x Does NOT = 4cos^3x-3cosx
Whereas 2cos^3x - cosx - 2cosx + 2cos^3x would

Thanks for any help!

Originally Posted by SMA777

cos (2x + x) =
cos2xcosx+sin2xsinx =

It's actually a sign instead (Second step.)

Originally Posted by Krizalid

It's actually a sign instead (Second step.)

Er... maybe I'm just being dense, but why?

Oh, I copied my Sum/Difference formula incorrectly! Got it. Thank you!