(A) Evaluate: 5/(cot^2 30^°)+1/(sin^2 60^°)- cot^2 45^°+2 sin^2 90^°

\[\begin{aligned} & \frac{5}{\cot ^{2} 30^{\circ}}+\frac{1}{\sin ^{2} 60^{\circ}}-\cot ^{2} 45^{\circ}+2 \sin ^{2} 90^{\circ} \\ & =\frac{5}{(\sqrt{3})^{2}}+\frac{1}{(\sqrt{3} / 2)^{2}}-(1)^{2}+2(1)^{2}=\frac{5}{3}+\frac{4}{3}-1+2 \\ & =\frac{9}{3}+1=4 \end{aligned} \]

\[\begin{aligned} & \sin \theta=\cos \theta \Rightarrow \frac{\sin \theta}{\cos \theta}=1 \Rightarrow \tan \theta=1 \Rightarrow \cot \theta=1 \\ & \tan ^{2} \theta+\cot ^{2} \theta-2=(1)^{2}+(1)^{2}-2=0 \end{aligned} \]