## anonymous one year ago Rewrite with only sin x and cos x. cos 3x Please help me understand this. It is so confusing to me

1. anonymous

Use the property of compound angles, in which $\cos3\theta=\cos(2\theta+\theta)$ You should also know that the expansion of$\cos2\theta=1-2\sin ^{2}\theta =2\cos ^{2}\theta-1$ Also in compound angles, use the property that:$\cos(A+B)=cosAcosB-sinAsinB$ Also take note that $\sin2\theta=2\sin \theta \cos \theta$ Moving onto the exercise, we get$\cos3x=\cos(2x+x)=\cos2xcosx - \sin2xsinx= (2\cos ^{2}x-1)cosx - (2sinxcosx)sinx$

2. anonymous

Further expanding, we get$2\cos ^{3}x-cosx - 2\sin ^{2}xcosx$

3. anonymous

that all makes sense but that matches none of the answers