Question

If A and B are acute angles such that sin (A - B)= cos(A+B) = 1/2, find A and B

Answer 1

cos(A+B)=1/2=cos 60
A+B=60 ---(1)

sin(A-B)=1/2=sin 30
A-B = 30 ---(2)

by adding eqn 1 and 2,
we get

A+B+A-B=60+30

2A=90

A=90/2=45

according to eqn 1 A+B=60

THEN,B=60-A=60-45=15

HENCE,A=45,B=15

Like if satisfied