cos 3x = 4 cos^3 x - 3 cos x

I need help on where to start.

galactus

Use the sum formula for cos,



Work on the left and try to turn it into the right.

Use the identities and



Sub them in and it should fall into place.

chris1080p

Thanks for your help.

galactus

You're welcome. Let me know if yo got it to work OK.

Oh yeah, if you don't mind, please click on 'rate this answer' for me.

chris1080p

So far I did what you said and arrived at:

cos^2 x - sin^2 x cosx - 2sinx cosx sinx

I know cos^2 x +sin^2 x=1, but I don't see how it falls into place.

Is there a way that I can work on the right side to equal the left aswell?

galactus

Well, let's continue then from where we left off.

I will make the identity subs

and



Then we get:



Expand:





Now, make the sub







There it is...

chris1080p

Thanks man for all of your help. Lol, I couldn't rate your answer again.

galactus

That's OK. I know. I hope this learned you what you gotta do to solve them. It is a matter of seeing the right identity substitutions. Mind you, there are certainly other ways to go about it.
Someone else may see a simpler way, but this worked well.