(A) Evaluate (5 cos^2 60^°+4 sec^2 30^°- tan^2 45^°)/(sin^2 30^°+ cos^2 30^°)

\[\begin{gathered} \frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}} \\ =\frac{5(1 / 2)^{2}+4(2 / \sqrt{3})^{2}-(1)^{2}}{1} \\ =\frac{5 / 4+16 / 3-1}{1}=\frac{67}{12} \end{gathered} \]

\[\begin{aligned} & \sin (\mathrm{A}-\mathrm{B})=0 \Rightarrow \mathrm{~A}-\mathrm{B}=0^{\circ} \\ & \cos (\mathrm{A}+\mathrm{B})=\frac{1}{2} \Rightarrow \mathrm{~A}+\mathrm{B}=60^{\circ} \\ & \Rightarrow \mathrm{A}=30^{\circ}, \mathrm{B}=30^{\circ} \end{aligned} \]