If $\cot(A + B) = 1$ and $\cot(A - B) = \sqrt{3}$ with $A, B$ acute, then $A = ?$

Since $\cot(A+B)=1$, $A+B=45^\circ$, and $\cot(A-B)=\sqrt3$ gives $A-B=30^\circ$. Adding yields $2A=75^\circ$, so $A=37.5^\circ$.