Question

Rewrite with only sin x and cos x.

cos 3x

Answer 1

\[\large \cos(3x)=\cos(2x+x)\]From here we can apply the Angle Addition Formula for Cosine.\[\large \cos(2x+x)=\color{cornflowerblue}{\cos(2x)}\cos x-\color{orangered}{\sin(2x)} \sin x\]And from here, we can apply the Cosine Double Angle Formula to the \(\color{cornflowerblue}{\cos(2x)}\) and the Sine Double Angle Formula to the \(\color{orangered}{\sin(2x)}\).\[\large =\left(\color{cornflowerblue}{\cos^2x-\sin^2x}\right)\cos x-\left(\color{orangered}{2\sin x \cos x}\right)\sin x\]
Andddd you can simplify it down a bit from here.
But everything is in terms of an Angle X instead of 2x or 3x now, so that's good!

Answer 2

Oh that's really annoying...
They said rewrite with ONLY sinx and cosx....
yet all of your multiple choices have sin2x or sin3x in them...

what a stupid question :\
Hmmmm

Answer 3

Oh maybe I'm reading it incorrectly because powers don't copy paste very well.

Like option number 1, is that suppose to be:
\[\large \cos x-4\cos x \sin^2x\]
Or\[\large \cos x-4\cos x \sin (2x)\]

Answer 4

I was asking a question....