# Math Help - Proving

1. ## Proving

Prove $
cos (2x+x) = 4cos^3x - 3cosx
$

2. Dear punch,

First expand Cos(2x+x) using,

$Cos{(2x+x)}=Cos{2x}Cos{x}-Sin{2x}Sin{x}$

Then use $Cos2x=2Cos^2x-1\mbox{ and }{Sin^2}x=1-{Cos^2}x$

3. Originally Posted by Punch
Prove $
cos (2x+x) = 4cos^3x - 3cosx
$

$cos(2x+x)=cos(2x)cos(x)-sin(2x)sin(x)$

$=(2cos^2(x)-1)cos(x)-2sin(x)cos(x)sin(x)$

$=2cos^3(x)-cos(x)-2cos(x)(1-cos^2(x))$

$=2cos^3(x)-cos(x)-2cos(x)+2cos^3(x)$

$
=4cos^3(x)-3cos(x)
$

4. Oh, thanks a lot guys, i was thinking about the extra sin^2 i had, now i know how to get rid of it by using identities...