Is it ever possible that cos (A−B)=cos ⁡A−cos ⁡B? Why or why not?

Answer:The given equation is never possible i.e cos ( A - B ) ≠ cos A - cos B Step-by-step explanation:Given as :Is cos ( A - B ) = cos A - cos B To check this possibility , Let us put the value of angle A and B on both side of equation Now, Let A = 60°    and  B = 30° From Left hand side equation cos ( A - B ) = cos ( 60°  - 30° )Or, cos ( A - B ) = cos 30°∴   cos ( A - B ) = [tex]\frac{\sqrt{3} }{2}[/tex]or, cos ( A - B ) = 0.866From Right hand side equation cos A - cos B  =  cos  60° - cos  30°  Or,  cos A - cos B  =   [tex]\frac{1}{2}[/tex] -  [tex]\frac{\sqrt{3} }{2}[/tex]∴,  cos A - cos B  = 0.5 - 0.866I.e  cos A - cos B  = - 0.366 So, Left hand side ≠ Right hand sideSince while equating the values of angle A and b in the given equation on both sides, we get that the value of both sides are not equal , Thus we can say that the given equation is not equal to each other .Hence given equation is never possible i.e cos ( A - B ) ≠ cos A - cos B Answer