Question

Prove that $cos3x=4co{s}^{3}x-3cosx$ .

Answer 1

To prove :

$cos3x=4co{s}^{3}x-3cosx$

Proof :

$cos3x=cos(2x+x)$

$=cos2xcosx-sin2xsinx$

$=(-1+2co{s}^{2}x)cosx-2cosxsinxsinx$

$=-cosx+2co{s}^{3}x-2si{n}^{2}xcosx$

$=-cosx+2co{s}^{3}x-2(1-co{s}^{2}x)cosx$

$=-3cosx+4co{s}^{3}x$

Hence, $cos3x=4co{s}^{3}x-3cosx$