Question

If sin(A-B) =1/2, cos(A+B)=1/2, 0°<A+B_<90°,A>B,find A and B

Answer 1

sin(A-B)=1/2
sin(A-B)=sin 30
A-B=30     equation no 1

cos (A+B)=1/2
cos(A+B)=cos 60
A+B=60     equation no 2

A-B=30
A+B=60
2A=90
A=45
substituting a in equation 1
B=15