Question

# If ( sin (A-B)=frac{1}{2}, cos (A+B)=frac{1}{2}, 0^{circ}B, ) find ( A ) and ( B )

Solution

( sin (A-B)=frac{1}{2}=sin left(30^{circ}right) & Rightarrow A-B=30^{circ} )

( cos (A+B)=frac{1}{2}=cos left(60^{circ}right)=A+B=60^{circ} )

( Rightarrow 2 A=90^{circ} Rightarrow A=45^{circ} quad & B=15^{circ} )