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

• Dec 29th 2010, 08:29 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, 10:14 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.

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

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