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?

Let sin x + sin y = cos x + cos y for all x, y ∈ ℝ. What is $\rm tan \left(\frac{x}{2}+\frac{y}{2}\right)$ equal to?

Let 4sin² x = 3, where 0 ≤ x ≤ π. What is tan3x equal to?

Let the equation sec x.cosec x = p have a solution, where p is a positive real number. What should be the smallest value of p?