Sin(A+B)=1
cos(A-B)=√3/2
We know sin-1 =90
A+B=90 (1)
cos (A-B)=√3/2
A-B=cos-1 √3/2
We know cos-1 √3/2=30
A-B=30 _ (2)
Solve (1) & (2)
A+B=90
A-B=30 add
2A=120
A=60 B=30