What can be the maximum and minimum values of (A+B) and (A-B) ?

A+B = sqrt(A^2 +B^2 + 2ABcos(theta))

A-B = sqrt(A^2 +B^2 - 2ABcos(theta))

Maximum value of cos(theta) can be 1 and minimum value can be -1. 

 

hence for maximum value of cos(theta) 

A+B = sqrt(A^2 +B^2 + 2AB) = A+B

A-B = sqrt(A^2 +B^2 - 2AB) = A-B

For minimum value of cos(theta)

A+B = sqrt(A^2 +B^2 -2AB) = A-B

A+B = sqrt(A^2 +B^2 - 2AB(-1)) = A+B

 

So, the maximum values of both A+B and A-B will be A+B (but for different values of cos(theta))

and the minimum values for both A+B and A-B would be A-B (again for different values of cos(theta))