Question

How to express cos 3x in terms of cosx

Answer 1

`\cos3x=\cos(x+2x)=\cos x\cos2x-\sin x\sin2x`

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

`=\cos^3x-\cos x\sin^2x-2\sin^2x\cos x`

`=\cos^3x-3\cos x\sin^2x`

`=\cos^3x-3\cos x(1-\cos^2x)`

`=\cos^3x+3\cos^3x-3\cos x`

`=4\cos^3x-3\cos x`