Question

Rewrite using only sine and cosine:
cos 3x

I did:
cos 3x
cos (2x+x)
cos (2x+x) = cos 2x cos x - sin 2x sin x
(???)cos x - 2sin^2 x cos x

What should cos 2x be rewritten as? There are multiple ways it can be rewritten, I just don't understand how to know which one should be used at which times.

Answer 1

@flixoe I don't understand the objective here. Your answer for cos(2x + x) is already in terms of sine and cosine. Isn't that what you want?

Answer 2

A)cos x - 4 cos x sin^2x

B) -sin^3x + 2 sin x cos x

C) -sin^2x + 2 sin x cos x

D) 2 sin^2x cos x - 2 sin x cos x

I don't want an answer yet though.

Cos 2x can be rewritten as:
cos^2x - sin^2x
2 cos^2x -1
1 - sin^2x

I guess it needs to be further simplified, but I don't know where to go after what I've done.

Answer 3

cos 3x
cos (2x+x)
cos (2x+x) = cos 2x cos x - sin 2x sin x
(cos^2x - sin^2x)cos x - 2sin^2 x cos x
(cos^3x - sin^2x cos x) - 2sin^2 x cos x

Here I would do:
cos^3x - 3sin^2x cos x

But this isn't any of the answers...? What am I doing incorrectly?