Question

Rewrite with only sin x and cos x.

cos 3x

Answer 1

I got to cos(2x+x)= cos2xcosx-sin2xsinx

Answer 2

thats a great start... so now you need to look at cos(2x) and sin(2x)

sin(2x) = 2sin(x)cos(x)

and

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

or one of the other variations.


and substitute and simplify

Answer 3

(cos^2x-sin^2x)(cosx)-(2sinxcosx)(sinx) ?

Answer 4

well done... now its just a case of distributing... for the answer..

Answer 5

(cos^3x-sin^2xcosx)(2sin^2xcosx) ?

Answer 6

almost you need a - sign and then collect like terms

\[\cos^3(x) - \sin^2(x) \cos(x) - 2\sin^2(x) \cos(x)\]

so just collect the like terms

Answer 7

cos^3x-3sin^2xcosx ?

Answer 8

yes, that's it... well done

Answer 9

But that's not one of my choices.

cos x - 4 cos x sin2x

-sin3x + 2 sin x cos x

-sin2x + 2 sin x cos x

2 sin2x cos x - 2 sin x cos x

Answer 10

ok... so look at \[\cos^3(x) = \cos^2(x) \times \cos(x)\]

and \[\cos^2(x) = 1 - \sin^2(x)\]

so you have

\[(1 -\sin^2(x))\cos(x) - 3\sin^2(x)\cos(x)\]

and then simplify

Answer 11

So the answer is cosx-4sin^2xcosx !
Thank you so much!

Answer 12

yes, thats the answer

thats ok... sorry for the long approach... the solution may have been quicker by choosing a different substitution for cos(2x)

but glad to help