**Solution:**

To prove this, we have to use **Sum & Difference Identities**.

LHS = **sin (45°+ A)cos (45°- B) + cos (45°+ A)sin (45°- B)**

= sin [(45°+ A)+(45°- B)]…… *{∵ sin (A + B) = sinA cosB + cosA sinB, A= 45°+ A, B= 45°- B }*

= sin [90**°**+(A-B)]…. *{∵ sin (90+θ) = cos θ}*

= **cos (A-B)**

= RHS