If sin(A + B) = 1 and 2 sin(A - B) = 1, where 0 < A, B < $\frac{\pi}{2}$, then what is tan A ∶ tan B equal to?

Consider a regular polygon with 10 sides. What is the number of triangles that can be formed by joining the vertices which have no common side with any of the sides of the polygon?

Consider all the real roots of the equation x⁴ - 10x² + 9 = 0. What is the sum of the absolute values of the roots?

Consider the expansion of (1 + x)ⁿ. Let p, q, r and s be the coefficients of first, second, nth and (n + 1)th terms respectively. What is (ps + qr) equal to?