Question

Rewrite with only sinx and cosx:

Sin3x + Cos 3x

-So far my work is
Cos3x
Cosx(cos2x)
cosx(cos^2x-sin^2x)
Cos^3x-Sin^2xCosx

and
Sin3x
Sinx(sin2x)
Sinx(2sinxcosx)

I'm not sure if its right but im mainly confused on what to do with the Sin3x

-Please help!!

Answer 1

for sin3x
sin3x=sin(2x+x)
and then use the rule
sin(A+B)=sin A cos B + cos A sin B

Answer 2

the answers for Sin3x:
2sinxcos^2x + cosx
2sinxCos^2x + sin^3x
sinxcos^2x - sin^3x ...and
2cos^2xsin + sinx

Answer 3

\[\sin(2x)\cos(x) + \cos(2x)\sin(x) + \cos(2x)\cos(x) - \sin(2x)\sin(x)\]\[2\sin x \cos^2x+(1-2\sin^2x)\sin x + (2\cos^2x-1)\cos x - 2\sin^2x \cos x\]\[2\sin x - 2\sin^3x + \sin x - 2\sin^3x+2\cos^3x-\cos x-2\cos x+2\cos^3x\]\[3(\sin x-\cos x)-4(\sin^3x-\cos^3x)\]