SOLUTION: Use one of the product-to-sum formulas to write the given product as a sum of sines or a sum of cosines. cos 6θ cos 2θ

Algebra ->  Trigonometry-basics -> SOLUTION: Use one of the product-to-sum formulas to write the given product as a sum of sines or a sum of cosines. cos 6θ cos 2θ      Log On


   

Question 1028367: Use one of the product-to-sum formulas to write the given
product as a sum of sines or a sum of cosines.
cos 6θ cos 2θ
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Add the two equations:

cos%28A%2BB%29+=+cos%28A%29cos%28B%29-sin%28A%29sin%28B%29
cos%28A-B%29+=+cos%28A%29cos%28B%29%2Bsin%28A%29sin%28B%29

Get
cos%28A%2BB%29%2Bcos%28A-B%29=2cos%28A%29cos%28B%29

Multiply both sides by 1/2

expr%281%2F2%29%28cos%28A%2BB%29%2Bcos%28A-B%29%5E%22%22%29=cos%28A%29cos%28B%29

Swap sides:

cos%28A%29cos%28B%29=expr%281%2F2%29%28cos%28A%2BB%29%2Bcos%28A-B%29%5E%22%22%29 <--product-to-sum formula

Let A=6theta, B=2theta





Edwin