Consider the following for the next items that follow:

Let sin x + sin y = √3 (cos y - cos x); x + y = $\rm \frac{\pi}{2}$, x < x, y < $\rm \frac{\pi}{2}$

What is a value of cos³ x + cos³ y?

Consider the following for the next items that follow:

The angles A, B and C of a triangle ABC are in the ratio 3 ∶ 5 ∶ 4.

What is the value of a + b + √2 c equal to ?

Consider the following for the next items that follow:

The angles A, B and C of a triangle ABC are in the ratio 3 ∶ 5 ∶ 4.

What is the ratio of a2 ∶ b2 ∶ c2 ?

What is the equation of directrix of parabola y2 = 4bx, where b < 0 and b2 + b - 2 = 0?