Double-Angle Simplification

1. Oct 13, 2012

MaoRaygo

1. The problem statement, all variables and given/known data
I've been having problems with a lot of identity problems lately, but I've found that I'm especially having issues with problems like this one;
Verify the identity,

1/2 Sin (4x) = 2SinxCosx-4Sin3xCosx

2. Relevant equations
My professor told me you use Sin(A-B)=SinACosB-CosASinB

3. The attempt at a solution
The best I could do was

1/2 Sin4x=2SinxCox-4Sin3xCos

1/2Sin4x=2(SinxCosx-2sin3)

1/2Sin4x=2Sin(x-4x)=-2Sin(3x)

I know that this is a horrible attempt at solving, but some help would be greatly appreciated.

2. Oct 13, 2012

CAF123

Start with the LHS and write $\frac{1}{2} \sin(4x)\,\,\text{as}\,\, \frac{1}{2} \sin(2x +2x)$ and expand using the addition formula as your professor suggested.