proving indentities..

**pop_91** · October 25th 2009, 02:45 AM

i cant quite seem to get this.. thanks for the help. x

Prove the following indenty. You may assume the formulas for sun2x and cos2x.

cos3x = 4cos(^3)x - 3cosx

**ramiee2010** · October 25th 2009, 02:52 AM

Originally Posted by pop_91

i cant quite seem to get this.. thanks for the help. x

Prove the following indenty. You may assume the formulas for sun2x and cos2x.

cos3x = 4cos(^3)x - 3cosx

cos (3x)=cos(x+2x)
use identity
cos (A+B)=cos B cos B-sin A sin B
cos 2A an sin 2A.
$\sin^2 x=1- \cos^2 x$

**pop_91** · October 25th 2009, 03:14 AM

i've done that and sub in 1-cos^2x but i dont get the correct answer

**ramiee2010** · October 25th 2009, 03:21 AM

Originally Posted by pop_91

i've done that and sub in 1-cos^2x but i dont get the correct answer

$\cos (3x)=\cos(x+2x)=\cos x \cos 2x-\sin x \sin 2x$
$=\cos x ( 2 \cos^2 x -1) - \sin x (2 \sin x \cos x)$
$=2 \cos^3 x -\cos x - 2 \sin^2 x \cos x$

put $\sin^2 x=1- \cos^2 x$

**pop_91** · October 25th 2009, 03:29 AM

ive got it now! thanks

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