# Multiplying cosines

1. Dec 29, 2011

### SMOF

Hello,

I hope everyone is well.

Also, I hope someone can help me understand something. I am trying to understand how cos(ω1t) times cos(ω2t) can be represented as

x(t) 1/2 (cos(ω2 - ω1)t) + 1/2 (cos(ω2 + ω1)t)

Thanks in advance for any help.

Seán

2. Dec 29, 2011

### Mentallic

Try expanding cos(A+B) and cos(A-B)

3. Dec 29, 2011

### SMOF

Hello,

So, cos(A+B) = cosA cosB - sinA sinB, and cos(A-B) = cosA cosB + sinA sinB.

But I don't see how this gets me to the solution I need, since it doesn't have a sin component.

But maybe I am just being stupid here.

Seán

4. Dec 29, 2011

### SMOF

Oh, I may have got it with the Product to Sum Identity.

Seán

5. Dec 30, 2011

### Mentallic

Ok notice that the cos(A+B) has a sinAsinB component and cos(A-B) has a -sinAsinB component, so why not add these two cosines sums to get rid of the sinAsinB?

6. Dec 31, 2011

### SMOF

Hello.

That will just leave me with 2(cosAcosB) ...yea?

Seán

7. Dec 31, 2011

8. Jan 2, 2012

### Mentallic

Right, and you want cosAcosB, so...

9. Jan 2, 2012

### SMOF

Hello.

Yea, so, I divide by 2 ...or, multiply by a half ...I think I have it from here.

Many thanks for your help :)

Seán

10. Jan 2, 2012

### Mentallic

Yep that's it

You're welcome, and good luck with your physics!