Find A and B if sin (A-B)=1/2=cos (A+B) and A, B are acute angles.

Dear student
sin(A-B)= sin30
(A-B)= 30 -(1)
cos(A+B)= cos60
(A+B)=60-(2)
On adding eq(1) and (2)
2A= 90
A= 45
From eq 1
B = A-30= 45-30=15
regards.