# Identity for cos(wt+phase)cos(wt)

• Dec 29th 2010, 07:29 PM
laguna92651
Identity for cos(wt+phase)cos(wt)
I am looking for an identity to simplify the following:

cos(wt+phase)cos(wt)=?

I assume it will be something similar to the power reduction identity:

cos^2(wt)=1/2(1+cos(2wt))

Thanks
• Dec 29th 2010, 09:14 PM
Sudharaka
Quote:

Originally Posted by laguna92651
I am looking for an identity to simplify the following:

cos(wt+phase)cos(wt)=?

I assume it will be something similar to the power reduction identity:

cos^2(wt)=1/2(1+cos(2wt))

Thanks

Dear laguna92651,

You can use the product to sum identity.

$\displaystyle \cos A\cos B=\frac{1}{2}\left[\cos(A+B)+\cos(A-B)\right]$

For a complete list of trignometric identities you can refer List of trigonometric identities - Wikipedia, the free encyclopedia

• Dec 29th 2010, 09:48 PM
laguna92651
I looked at that identity many times, but having the phase as part of one of the functions threw me. But all of sudden with your replay, I could see it clearly for some reason. It didn't dawn on me what A and B represented I guess, made it way harder than it was.

I got what I would expect, this is an amplitude modulation problem I was working on.
cos(wt+phase)cos(wt)=1/2[cos(2wt+phase)+cos(phase)

Thanks