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? 

For what value of θ, where 0 < θ < $\frac{\pi}{2}$, does sin θ + sin θ cos θ maximum value?