Prove the following: sin(n+1)xsin(n+2)x + cos(n+1)xcos(n+2)x = cosx

Use cosAcosB + sinAsinB = cos(A-B)
LHS = sin(n+1)xsin(n+2)x + cos(n+1)xcos(n+2)x
= cos[(n+2)x - (n+1)x]
= cosx
= RHS
Hence proved.