Question

Rewrite with only sin x and cos x. cos 3x
Please help me understand this. It is so confusing to me

Answer 1

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\[\cos3x=\cos(2x+x)=\cos2xcosx - \sin2xsinx= (2\cos ^{2}x-1)cosx - (2sinxcosx)sinx\]

Answer 2

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

Answer 3

that all makes sense but that matches none of the answers