The problem asks me to show that the addition of two cosines with different wavelength and frequencies gives a solution with beats. Mathematically, I need to verify that A cos (k1x-w1t)+A cos (k2x-w2t) is equivalent to A cos (.5(k1+k2)x-.5(w1+w2)t) cos (.5(k1-k2)x-.5(w1-w2)t) I converted the second equation into exponential form (cos (kx-wt)=1/2(e^i(kx-wt)+e^-i(kx-wt)), multiplied the resulting binomials together, and simplified to get the first equation. My problem is with the constant, A. How do I deal with it? I need A/2 for the first equation, but simplication of the second yields A/4. How to resolve this? Any help greatly appreciated!!