1. ## 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

2. 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.

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

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

3. 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

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# cos(wt)cos^2(wt)

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