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Math Help - Identity for cos(wt+phase)cos(wt)

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by laguna92651 View Post
    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

    Hope this will help you.
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  3. #3
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    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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