The value of sinA+sinB=x and cosA+cosB=y then cos(A–B)=
x2+y2+22
x2−y2+22
x2+y2−22
y2−x2+22
sinA+sinB=x
Squaring on both sides
cosA+cosB=y
Adding two functions
2cos(A−B)=x2+y2−2
cos(A−B)=x2+y2−22