Can cos(A−B)=cos ⁡A−cos ⁡B?

Question

Is it ever possible that coscos ⁡cos ⁡

Answer 1

cos(A-B) = cosAcosB+sinAsinB.

So if cos(A-B)=cosA-cosB, cosB=1 and sinAsinB=-cosB

B=0, sinB = 0 and cosB = 1; so cos(A-B) = cosA(1)-sinA(0) = cosA

Answer 2

Try 45 degrees and 90 degrees

cos(45-90) = cos(45) - cos(90) or

cos(-45) = cos(45) - 0 or

cos (45) = cos(45)