Question

How to express cos 3x in terms of cosx

Answer 1

$\cos3x=\cos(x+2x)=\cos x\cos2x-\sin x\sin2x$
$=\cos x(\cos^2x-\sin^2x)-2\sin^2x\cos x$
$=\cos^3x-\cos x\sin^2x-2\sin^2x\cos x$
$=\cos^3x-3\cos x\sin^2x$
$=\cos^3x-3\cos x(1-\cos^2x)$
$=\cos^3x+3\cos^3x-3\cos x$
$=4\cos^3x-3\cos x$