How do you use the sum to product formulas to write the sum or difference cos6x+cos2x as a product?

1 Answer
Apr 12, 2017

cos(6x)+cos(2x)=2cos4xcos2x

Explanation:

cos(A+B) + cos(A-B) = 2cosAcosB
Thus by comparing the left side of the above equation with the one we are given, we see that A+B=6x and A-B=2x

Solving simultaneously, we see that A=4x and B=2x

Thus, cos(6x)+cos(2x)=2cos4xcos2x

PROOF OF THIS SUM TO PRODUCT:
cos(A+B) + cos(A-B) = cosAcosB - sinAsinB + cosAcosB + sinAsinB
=2cosAcosB