Two bodies are projected from the same point with equal speeds in such directions that they both strike the same point on a plane whose inclination is `beta`. If `alpha` the angle of projection of the first body with the horizontal , show that the ratio of their time of flights is `(sin (alpha - beta))/(cos alpha)`

Explanation

To solve the problem, we need to find the ratio of the time of flights of two bodies projected from the same point with equal speeds, where the first body is projected at an angle \(\alpha\) and the second body strikes the same point on a plane inclined at an angle \(\beta\).

### Step 1: Understanding the Problem
We have two bodies projected with the same initial speed \(u\). The first body is projected at an angle \(\alpha\) with the horizontal, and the second body is projected at an angle \(\theta\) such that both bodies strike the same point on the inclined plane.

### Step 2: Range of the Projectiles
The range \(R\) of a projectile on an inclined plane can be expressed as:
\[
...